1
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Yamaguchi H, Murakami H. The multi-aspect tests in the presence of ties. Comput Stat Data Anal 2023. [DOI: 10.1016/j.csda.2022.107680] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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2
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Gonçalves ADS, Fernandes LHS, Nascimento ADC. Dynamics diagnosis of the COVID-19 deaths using the Pearson diagram. CHAOS, SOLITONS, AND FRACTALS 2022; 164:112634. [PMID: 36118941 PMCID: PMC9464589 DOI: 10.1016/j.chaos.2022.112634] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/03/2022] [Revised: 08/21/2022] [Accepted: 08/27/2022] [Indexed: 06/15/2023]
Abstract
The pandemic COVID-19 brings with it the need for studies and tools to help those in charge make decisions. Working with classical time series methods such as ARIMA and SARIMA has shown promising results in the first studies of COVID-19. We advance in this branch by proposing a risk factor map induced by the well-known Pearson diagram based on multivariate kurtosis and skewness measures to analyze the dynamics of deaths from COVID-19. In particular, we combine bootstrap for time series with SARIMA modeling in a new paradigm to construct a map on which one can analyze the dynamics of a set of time series. The proposed map allows a risk analysis of multiple countries in the four different periods of the pandemic COVID-19 in 55 countries. Our empirical evidence suggests a direct relationship between the multivariate skewness and kurtosis. We observe that the multivariate kurtosis increase leads to the rise of the multivariate skewness. Our findings reveal that the countries with high risk from the behavior of the number of deaths tend to have pronounced skewness and kurtosis values.
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Affiliation(s)
- Alan D S Gonçalves
- Departamento de Estatssca, Universidade Federal de Pernambuco, Recife, PE, 50670-901, Brazil
| | - Leonardo H S Fernandes
- Department of Economics and Informatics, Federal Rural University of Pernambuco, Serra Talhada, PE, 56909-535, Brazil
| | - Abraão D C Nascimento
- Departamento de Estatssca, Universidade Federal de Pernambuco, Recife, PE, 50670-901, Brazil
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3
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Efficient and robust estimation for autoregressive regression models using shape mixtures of skewt normal distribution. Methodol Comput Appl Probab 2022. [DOI: 10.1007/s11009-021-09872-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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4
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Use of calibration constraints and linear moments for variance estimation under stratified adaptive cluster sampling. Soft comput 2022. [DOI: 10.1007/s00500-022-07430-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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5
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Kitani M, Murakami H. One-sample location test based on the sign and Wilcoxon signed-rank tests. J STAT COMPUT SIM 2021. [DOI: 10.1080/00949655.2021.1968399] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Masato Kitani
- Department of Applied Mathematics, Graduate School of Science, Tokyo University of Science, Tokyo, Japan
| | - Hidetoshi Murakami
- Department of Applied Mathematics, Tokyo University of Science, Tokyo, Japan
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6
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Aslam M, Albassam M. Testing the normality of heart associated variables having neutrosophic numbers. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2021. [DOI: 10.3233/jifs-210375] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
In this paper, tests of skewness and kurtosis are introduced under neutrosophic statistics. The necessary measures and neutrosophic forms of these estimators are introduced. The application of the proposed tests is given using the data associated with heart diseases. From the real example analysis, the proposed tests are quite flexible and informative than the existing tests under classical statistics. In addition, it is concluded from the analysis that the proposed tests give information about the measure of indeterminacy in the presence of uncertainty.
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Affiliation(s)
- Muhammad Aslam
- Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
| | - Mohammed Albassam
- Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
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7
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Affiliation(s)
- Po-Ling Loh
- Department of Pure Mathematics and Mathematical Statistics University of Cambridge
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8
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Laha N. Adaptive estimation in symmetric location model under log-concavity constraint. Electron J Stat 2021. [DOI: 10.1214/21-ejs1852] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Nilanjana Laha
- Department of Biostatistics, Harvard University, 677 Huntington Ave, Boston, MA 02115, U.S.A
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9
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Lambert JW, Hawk GS. Identifying Pareto-based solutions for regression subset selection via a feasible solution algorithm. INTERNATIONAL JOURNAL OF DATA SCIENCE AND ANALYTICS 2020. [DOI: 10.1007/s41060-020-00218-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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10
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Punzo A, Bagnato L. The multivariate tail-inflated normal distribution and its application in finance. J STAT COMPUT SIM 2020. [DOI: 10.1080/00949655.2020.1805451] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Antonio Punzo
- Dipartimento di Economia e Impresa, Università degli Studi di Catania, Catania, Italy
| | - Luca Bagnato
- Dipartimento di Scienze Economiche e Sociali, Università Cattolica del Sacro Cuore, Piacenza, Italy
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11
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Mohammed MB, Adam MB, Ali N, Zulkafli HS. Improved frequency table’s measures of skewness and kurtosis with application to weather data. COMMUN STAT-THEOR M 2020. [DOI: 10.1080/03610926.2020.1752386] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- M. B. Mohammed
- Mathematics and Computer Science, Federal University of Kashere, Kashere, Nigeria
| | - M. B. Adam
- Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Malaysia
| | - N. Ali
- Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Malaysia
| | - H. S. Zulkafli
- Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Malaysia
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12
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Punzo A, Bagnato L. Allometric analysis using the multivariate shifted exponential normal distribution. Biom J 2020; 62:1525-1543. [PMID: 32240556 DOI: 10.1002/bimj.201900248] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2019] [Revised: 01/30/2020] [Accepted: 02/02/2020] [Indexed: 11/10/2022]
Abstract
In allometric studies, the joint distribution of the log-transformed morphometric variables is typically elliptical and with heavy tails. To account for these peculiarities, we introduce the multivariate shifted exponential normal (MSEN) distribution , an elliptical heavy-tailed generalization of the multivariate normal (MN). The MSEN belongs to the family of MN scale mixtures (MNSMs) by choosing a convenient shifted exponential as mixing distribution. The probability density function of the MSEN has a simple closed-form characterized by only one additional parameter, with respect to the nested MN, governing the tail weight. The first four moments exist and the excess kurtosis can assume any positive value. The membership to the family of MNSMs allows us a simple computation of the maximum likelihood (ML) estimates of the parameters via the expectation-maximization (EM) algorithm; advantageously, the M-step is computationally simplified by closed-form updates of all the parameters. We also evaluate the existence of the ML estimates. Since the parameter governing the tail weight is estimated from the data, robust estimates of the mean vector of the nested MN distribution are automatically obtained by downweighting; we show this aspect theoretically but also by means of a simulation study. We fit the MSEN distribution to multivariate allometric data where we show its usefulness also in comparison with other well-established multivariate elliptical distributions.
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Affiliation(s)
- Antonio Punzo
- Dipartimento di Economia e Impresa, Università di Catania, Catania, Sicilia, Italy
| | - Luca Bagnato
- Dipartimento di Scienze Economiche e Sociali, Università Cattolica del Sacro Cuore, Piacenza, Emilia-Romagna, Italy
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13
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Bias, Precision, and Accuracy of Skewness and Kurtosis Estimators for Frequently Used Continuous Distributions. Symmetry (Basel) 2019. [DOI: 10.3390/sym12010019] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Several measures of skewness and kurtosis were proposed by Hogg (1974) in order to reduce the bias of conventional estimators when the distribution is non-normal. Here we conducted a Monte Carlo simulation study to compare the performance of conventional and Hogg’s estimators, considering the most frequent continuous distributions used in health, education, and social sciences (gamma, lognormal and exponential distributions). In order to determine the bias, precision and accuracy of the skewness and kurtosis estimators for each distribution we calculated the relative bias, the coefficient of variation, and the scaled root mean square error. The effect of sample size on the estimators is also analyzed. In addition, a SAS program for calculating both conventional and Hogg’s estimators is presented. The results indicated that for the non-normal distributions investigated, the estimators of skewness and kurtosis which best reflect the shape of the distribution are Hogg’s estimators. It should also be noted that Hogg’s estimators are not as affected by sample size as are conventional estimators.
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14
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Punzo A, Tortora C. Multiple scaled contaminated normal distribution and its application in clustering. STAT MODEL 2019. [DOI: 10.1177/1471082x19890935] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
The multivariate contaminated normal (MCN) distribution represents a simple heavy-tailed generalization of the multivariate normal (MN) distribution to model elliptical contoured scatters in the presence of mild outliers (also referred to as ‘bad’ points herein) and automatically detect bad points. The price of these advantages is two additional parameters: proportion of good observations and degree of contamination. However, in a multivariate setting, only one proportion of good observations and only one degree of contamination may be limiting. To overcome this limitation, we propose a multiple scaled contaminated normal (MSCN) distribution. Among its parameters, we have an orthogonal matrix Γ. In the space spanned by the vectors (principal components) of Γ, there is a proportion of good observations and a degree of contamination for each component. Moreover, each observation has a posterior probability of being good with respect to each principal component. Thanks to this probability, the method provides directional robust estimates of the parameters of the nested MN and automatic directional detection of bad points. The term ‘directional’ is added to specify that the method works separately for each principal component. Mixtures of MSCN distributions are also proposed, and an expectation-maximization algorithm is used for parameter estimation. Real and simulated data are considered to show the usefulness of our mixture with respect to well-established mixtures of symmetric distributions with heavy tails.
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Affiliation(s)
- Antonio Punzo
- Department of Economics and Business, University of Catania, Catania, Italy
| | - Cristina Tortora
- Department of Mathematics and Statistics, San José State University, San José, CA, USA
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15
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Büning H. An adaptive distribution-free test for the general two-sample problem. Comput Stat 2019. [DOI: 10.1007/s001800200108] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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16
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Doğru FZ, Bulut YM, Arslan O. Doubly reweighted estimators for the parameters of the multivariate t-distribution. COMMUN STAT-THEOR M 2018. [DOI: 10.1080/03610926.2018.1445861] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Affiliation(s)
| | - Y. Murat Bulut
- Department of Statistics, Eskişehir Osmangazi University, Eskişehir, Turkey
| | - Olcay Arslan
- Department of Statistics, Ankara University, Ankara, Turkey
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17
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Scheinhardt MO, Ziegler A. Location Tests for Biomarker Studies: A Comparison Using Simulations for the Two-sample Case. Methods Inf Med 2018; 52:351-9. [DOI: 10.3414/me12-02-0014] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2012] [Accepted: 06/09/2013] [Indexed: 11/09/2022]
Abstract
Summary
Background: Gene, protein, or metabolite expression levels are often non-normally distributed, heavy tailed and contain outliers. Standard statistical approaches may fail as location tests in this situation.
Objectives: In three Monte-Carlo simulation studies, we aimed at comparing the type I error levels and empirical power of standard location tests and three adaptive tests [O’Gorman, Can J Stat 1997; 25: 269 –279; Keselman et al., Brit J Math Stat Psychol 2007; 60: 267– 293; Szymczak et al., Stat Med 2013; 32: 524 – 537] for a wide range of distributions.
Methods: We simulated two-sample scena -rios using the g-and-k-distribution family to systematically vary tail length and skewness with identical and varying variability between groups.
Results: All tests kept the type I error level when groups did not vary in their variability. The standard non-parametric U-test per -formed well in all simulated scenarios. It was outperformed by the two non-parametric adaptive methods in case of heavy tails or large skewness. Most tests did not keep the type I error level for skewed data in the case of heterogeneous variances.
Conclusions: The standard U-test was a powerful and robust location test for most of the simulated scenarios except for very heavy tailed or heavy skewed data, and it is thus to be recommended except for these cases. The non-parametric adaptive tests were powerful for both normal and non-normal distributions under sample variance homogeneity. But when sample variances differed, they did not keep the type I error level. The parametric adaptive test lacks power for skewed and heavy tailed distributions.
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Abstract
Unit-level logistic regression models with mixed effects have been used for estimating small area proportions in the literature. Normality is commonly assumed for the random effects. Nonetheless, real data often show significant departures from normality assumptions of the random effects. To reduce the risk of model misspecification, we propose an adaptive hierarchical Bayes estimation approach in which the distribution of the random effect is chosen adaptively from the exponential power class of probability distributions. The richness of the exponential power class ensures the robustness of our hierarchical Bayes approach against departure from normality. We demonstrate the robustness of our proposed model using both simulated and real data. The results suggest that the proposed model works reasonably well to incorporate potential kurtosis of the random effects distribution.
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Affiliation(s)
- Benmei Liu
- Division of Cancer Control and Population Sciences, National Cancer Institute, Medical Center Drive, Bethesda, MD, USA
| | - Partha Lahiri
- University of Maryland, Lefrak Hall, College Park, MD, USA
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19
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Cornell JE, Young DM, Seaman SL, Kirk RE. Power Comparisons of Eight Tests for Sphericity in Repeated Measures Designs. ACTA ACUST UNITED AC 2016. [DOI: 10.3102/10769986017003233] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
A Monte Carlo simulation was conducted to investigate the relative power of eight tests for sphericity in randomized block designs. Box’s (1954) epsilon values º = .35, .55, .75, .80, .85, .90, .95, and 1.00 were used to quantify departures from sphericity for rank-1 population covariance matrices of dimension p = 3, 5, 7, and 9. Sample covariance matrices were generated for samples of size n = 10, 15, 20, and 30. The locally best invariant test demonstrated substantial power to detect departures from sphericity—regardless of p— for both small and large samples for rank-1 alternatives. Recommendations are made regarding the use of preliminary tests.
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Abstract
It is noted that the usual estimators that are optimal under a Gaussian assumption are very vulnerable to the effects of outliers. A survey of robust alternatives to the mean, standard deviation, product moment correlation, t-test, and analysis of variance is offered. Robust methods of factor analysis, principal components analysis and multivariate analysis of variance are also surveyed, as are schemes for outlier detection.
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21
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Abstract
This article considers the problem of comparing two independent groups in terms of some measure of location. It is well known that with Student's two-independent-sample t test, the actual level of significance can be well above or below the nominal level, confidence intervals can have inaccurate probability coverage, and power can be low relative to other methods. A solution to deal with heterogeneity is Welch's (1938) test. Welch's test deals with heteroscedasticity but can have poor power under arbitrarily small departures from normality. Yuen (1974) generalized Welch's test to trimmed means; her method provides improved control over the probability of a Type I error, but problems remain. Transformations for skewness improve matters, but the probability of a Type I error remains unsatisfactory in some situations. We find that a transformation for skewness combined with a bootstrap method improves Type I error control and probability coverage even if sample sizes are small.
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Affiliation(s)
- H J Keselman
- University of Manitoba, Winnipeg, Manitoba, Canada.
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22
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Hao L, Houser D. Adaptive Procedures for the Wilcoxon–Mann–Whitney Test: Seven Decades of Advances. COMMUN STAT-THEOR M 2015. [DOI: 10.1080/03610926.2012.762394] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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23
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Garibaldi S, Frisoli K, Ke L, Lim M. Lottery spending: a non-parametric analysis. PLoS One 2015; 10:e0115730. [PMID: 25642699 PMCID: PMC4314186 DOI: 10.1371/journal.pone.0115730] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2014] [Accepted: 12/01/2014] [Indexed: 11/18/2022] Open
Abstract
We analyze the spending of individuals in the United States on lottery tickets in an average month, as reported in surveys. We view these surveys as sampling from an unknown distribution, and we use non-parametric methods to compare properties of this distribution for various demographic groups, as well as claims that some properties of this distribution are constant across surveys. We find that the observed higher spending by Hispanic lottery players can be attributed to differences in education levels, and we dispute previous claims that the top 10% of lottery players consistently account for 50% of lottery sales.
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Affiliation(s)
- Skip Garibaldi
- Institute for Pure and Applied Mathematics, UCLA, 460 Portola Plaza, Box 957121, Los Angeles, California 90095-7121, USA
- Department of Mathematics & Computer Science, Emory University, 400 Dowman Dr, Atlanta, Georgia 30322, USA
- * E-mail:
| | - Kayla Frisoli
- Institute for Pure and Applied Mathematics, UCLA, 460 Portola Plaza, Box 957121, Los Angeles, California 90095-7121, USA
| | - Li Ke
- Institute for Pure and Applied Mathematics, UCLA, 460 Portola Plaza, Box 957121, Los Angeles, California 90095-7121, USA
| | - Melody Lim
- Institute for Pure and Applied Mathematics, UCLA, 460 Portola Plaza, Box 957121, Los Angeles, California 90095-7121, USA
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24
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Corlu CG, Meterelliyoz M. Estimating the Parameters of the Generalized Lambda Distribution: Which Method Performs Best? COMMUN STAT-SIMUL C 2015. [DOI: 10.1080/03610918.2014.901355] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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25
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Too good to be true: rhesus monkeys react negatively to better-than-expected offers. PLoS One 2013; 8:e75768. [PMID: 24130742 PMCID: PMC3794042 DOI: 10.1371/journal.pone.0075768] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2013] [Accepted: 08/18/2013] [Indexed: 11/19/2022] Open
Abstract
To succeed in a dynamically changing world, animals need to predict their environments. Humans, in fact, exhibit such a strong desire for consistency that one of the most well-established findings in social psychology is the effort people make to maintain consistency among their beliefs, attitudes, and behavior. However, displeasure with unpredictability leads to a potential paradox, because a positive outcome that exceeds one's expectations often leads to increased subjective value and positive affect, not the opposite. We tested the hypothesis that two evolutionarily-conserved evaluation processes underlie goal-directed behavior: (1) consistency, concerned with prediction errors, and (2) valuation, concerned with outcome utility. Rhesus monkeys (Macaca mulatta) viewed a food item and then were offered an identical, better, or worse food, which they could accept or reject. The monkeys ultimately accepted all offers, attesting to the influence of the valuation process. However, they were slower to accept the unexpected offers, and they exhibited aversive reactions, especially to the better-than-expected offers, repeatedly turning their heads and looking away before accepting the food item. Our findings (a) provide evidence for two separable evaluation processes in primates, consistency and value assessment, (b) reveal a direct relationship between consistency assessment and emotional processes, and (c) show that our wariness with events that are much better than expected is shared with other social primates.
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Blanca MJ, Arnau J, López-Montiel D, Bono R, Bendayan R. Skewness and Kurtosis in Real Data Samples. METHODOLOGY-EUROPEAN JOURNAL OF RESEARCH METHODS FOR THE BEHAVIORAL AND SOCIAL SCIENCES 2013. [DOI: 10.1027/1614-2241/a000057] [Citation(s) in RCA: 187] [Impact Index Per Article: 17.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022] Open
Abstract
Parametric statistics are based on the assumption of normality. Recent findings suggest that Type I error and power can be adversely affected when data are non-normal. This paper aims to assess the distributional shape of real data by examining the values of the third and fourth central moments as a measurement of skewness and kurtosis in small samples. The analysis concerned 693 distributions with a sample size ranging from 10 to 30. Measures of cognitive ability and of other psychological variables were included. The results showed that skewness ranged between −2.49 and 2.33. The values of kurtosis ranged between −1.92 and 7.41. Considering skewness and kurtosis together the results indicated that only 5.5% of distributions were close to expected values under normality. Although extreme contamination does not seem to be very frequent, the findings are consistent with previous research suggesting that normality is not the rule with real data.
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Affiliation(s)
- María J. Blanca
- Faculty of Psychology, Department of Psychobiology and Methodology, University of Malaga, Spain
| | - Jaume Arnau
- Faculty of Psychology, Department of Behavioural Sciences Methodology, University of Barcelona, Spain
| | - Dolores López-Montiel
- Faculty of Psychology, Department of Psychobiology and Methodology, University of Malaga, Spain
| | - Roser Bono
- Faculty of Psychology, Department of Behavioural Sciences Methodology, University of Barcelona, Spain
| | - Rebecca Bendayan
- Faculty of Psychology, Department of Psychobiology and Methodology, University of Malaga, Spain
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27
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Thas O, Clement L, Rayner JCW, Carvalho B, Van Criekinge W. An omnibus consistent adaptive percentile modified Wilcoxon rank sum test with applications in gene expression studies. Biometrics 2012; 68:446-54. [PMID: 22506868 DOI: 10.1111/j.1541-0420.2012.01750.x] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present an adaptive percentile modified Wilcoxon rank sum test for the two-sample problem. The test is basically a Wilcoxon rank sum test applied on a fraction of the sample observations, and the fraction is adaptively determined by the sample observations. Most of the theory is developed under a location-shift model, but we demonstrate that the test is also meaningful for testing against more general alternatives. The test may be particularly useful for the analysis of massive datasets in which quasi-automatic hypothesis testing is required. We investigate the power characteristics of the new test in a simulation study, and we apply the test to a microarray experiment on colorectal cancer. These empirical studies demonstrate that the new test has good overall power and that it succeeds better in finding differentially expressed genes as compared to other popular tests. We conclude that the new nonparametric test is widely applicable and that its power is comparable to the power of the Baumgartner-Weiß-Schindler test.
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Affiliation(s)
- Olivier Thas
- Department of Mathematical Modeling, Statistics and Bioinformatics, Ghent University, Coupure Links 653, B-9000 Gent, Belgium.
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28
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Rosenbaum PR. An exact adaptive test with superior design sensitivity in an observational study of treatments for ovarian cancer. Ann Appl Stat 2012. [DOI: 10.1214/11-aoas508] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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29
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Rocke DM, Downs GW. Estimating the variances of robust estimators of location: influence curve, jackknife and bootstrap. COMMUN STAT-SIMUL C 2010. [DOI: 10.1080/03610918108812204] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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30
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31
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Cooray K, Ananda MM. Analyzing survival data with highly negatively skewed distribution: The Gompertz-sinh family. J Appl Stat 2009. [DOI: 10.1080/02664760802663072] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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32
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Keselman HJ, Wilcox RR, Algina J, Othman AR, Fradette K. A comparative study of robust tests for spread: asymmetric trimming strategies. THE BRITISH JOURNAL OF MATHEMATICAL AND STATISTICAL PSYCHOLOGY 2008; 61:235-253. [PMID: 18433520 DOI: 10.1348/000711008x299742] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
We examined 633 procedures that can be used to compare the variability of scores across independent groups. The procedures, except for one, were modifications of the procedures suggested by Levene (1960) and O'Brien (1981). We modified their procedures by substituting robust measures of the typical score and variability, rather than relying on classical estimators. The robust measures that we utilized were either based on a priori or empirically determined symmetric or asymmetric trimming strategies. The Levene-type and O'Brien-type transformed scores were used with either the ANOVA F test, a robust test due to Lee and Fung (1985), or the Welch (1951) test. Based on four measures of robustness, we recommend a Levene-type transformation based upon empirically determined 20% asymmetric trimmed means, involving a particular adaptive estimator, where the transformed scores are then used with the ANOVA F test.
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Affiliation(s)
- H J Keselman
- University of Manitoba, Winnipeg, Manitoba, Canada.
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Büning H, Rietz M. Adaptive bootstrap tests and its competitors in the c-sample scale problem. J Appl Stat 2008. [DOI: 10.1080/02664760802124257] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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CLARKE BRENTONR. EMPIRICAL EVIDENCE FOR ADAPTIVE CONFIDENCE INTERVALS AND IDENTIFICATION OF OUTLIERS USING METHODS OF TRIMMING. ACTA ACUST UNITED AC 2008. [DOI: 10.1111/j.1467-842x.1994.tb00637.x] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Zheng G, Ng HKT. Genetic model selection in two-phase analysis for case-control association studies. Biostatistics 2007; 9:391-9. [PMID: 18003629 DOI: 10.1093/biostatistics/kxm039] [Citation(s) in RCA: 63] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Abstract
The Cochran-Armitage trend test (CATT) is well suited for testing association between a marker and a disease in case-control studies. When the underlying genetic model for the disease is known, the CATT optimal for the genetic model is used. For complex diseases, however, the genetic models of the true disease loci are unknown. In this situation, robust tests are preferable. We propose a two-phase analysis with model selection for the case-control design. In the first phase, we use the difference of Hardy-Weinberg disequilibrium coefficients between the cases and the controls for model selection. Then, an optimal CATT corresponding to the selected model is used for testing association. The correlation of the statistics used for selection and the test for association is derived to adjust the two-phase analysis with control of the Type-I error rate. The simulation studies show that this new approach has greater efficiency robustness than the existing methods.
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Affiliation(s)
- Gang Zheng
- Office of Biostatistics Research, National Heart, Lung and Blood Institute, 6701 Rockledge Drive, Bethesda, MD 20892-7931, USA
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Keselman HJ, Wilcox RR, Lix LM, Algina J, Fradette K. Adaptive robust estimation and testing. THE BRITISH JOURNAL OF MATHEMATICAL AND STATISTICAL PSYCHOLOGY 2007; 60:267-293. [PMID: 17971270 DOI: 10.1348/000711005x63755] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
We examined nine adaptive methods of trimming, that is, methods that empirically determine when data should be trimmed and the amount to be trimmed from the tails of the empirical distribution. Over the 240 empirical values collected for each method investigated, in which we varied the total percentage of data trimmed, sample size, degree of variance heterogeneity, pairing of variances and group sizes, and population shape, one method resulted in exceptionally good control of Type I errors. However, under less extreme cases of non-normality and variance heterogeneity a number of methods exhibited reasonably good Type I error control. With regard to the power to detect non-null treatment effects, we found that the choice among the methods depended on the degree of non-normality and variance heterogeneity. Recommendations are offered.
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Affiliation(s)
- H J Keselman
- Department of Psychology, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2.
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MacGiliivray H. Skewness properties of asymmetric foems of tu1cey lambda distributions. COMMUN STAT-THEOR M 2007. [DOI: 10.1080/03610928208828385] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Waikar V, Schuurmann F, Raghunathan T. On a two stage shrinkage testimator of the mean of a normal distribution. COMMUN STAT-THEOR M 2007. [DOI: 10.1080/03610928408828802] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Affiliation(s)
- P.J. Do Jongh
- a Institute for Maritime Technology , P O Box 18, Simon's Town , 7995 , South Africa
| | - T. De Wet
- a Institute for Maritime Technology , P O Box 18, Simon's Town , 7995 , South Africa
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Pandey BN, Malik HJ. Shrinkage testimators for the shape parameter of weibull distributin under type ii censoring. COMMUN STAT-THEOR M 2007. [DOI: 10.1080/03610928908829960] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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