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Qasim M, Akram MN, Amin M, Månsson K. A restricted gamma ridge regression estimator combining the gamma ridge regression and the restricted maximum likelihood methods of estimation. J STAT COMPUT SIM 2021. [DOI: 10.1080/00949655.2021.2005063] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Muhammad Qasim
- Department of Economics, Finance and Statistics, Jönköping International Business School, Jönköping University, Jönköping, Sweden
| | | | - Muhammad Amin
- Department of Statistics, University of Sargodha, Sargodha, Pakistan
| | - Kristofer Månsson
- Department of Economics, Finance and Statistics, Jönköping International Business School, Jönköping University, Jönköping, Sweden
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Qasim M, Månsson K, Sjölander P, Kibria BMG. A new class of efficient and debiased two-step shrinkage estimators: method and application. J Appl Stat 2021; 49:4181-4205. [DOI: 10.1080/02664763.2021.1973389] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Muhammad Qasim
- Department of Economics, Finance and Statistics, Jönköping University, Jönköping, Sweden
| | - Kristofer Månsson
- Department of Economics, Finance and Statistics, Jönköping University, Jönköping, Sweden
| | - Pär Sjölander
- Department of Economics, Finance and Statistics, Jönköping University, Jönköping, Sweden
| | - B. M. Golam Kibria
- Department of Mathematics and Statistics, Florida International University, Miami, FL, USA
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Alheety MI, Månsson K, Golam Kibria BM. A new kind of stochastic restricted biased estimator for logistic regression model. J Appl Stat 2021; 48:1559-1578. [PMID: 35706568 PMCID: PMC9042162 DOI: 10.1080/02664763.2020.1769576] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
In the logistic regression model, the variance of the maximum likelihood estimator is inflated and unstable when the multicollinearity exists in the data. There are several methods available in literature to overcome this problem. We propose a new stochastic restricted biased estimator. We study the statistical properties of the proposed estimator and compare its performance with some existing estimators in the sense of scalar mean squared criterion. An example and a simulation study are provided to illustrate the performance of the proposed estimator.
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Affiliation(s)
- M. I. Alheety
- Department of Mathematics, College of Education for Pure Sciences, University of Anbar, Ramadi, Iraq
| | - Kristofer Månsson
- Department of Economics, Finance and Statistics, Jönköping University, Jonkoping, Sweden
| | - B. M. Golam Kibria
- Department of Mathematics and Statistics, Florida International University, Miami, FL, USA
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Omer T, Sjölander P, Månsson K, Kibria BMG. Improved estimators for the zero-inflated Poisson regression model in the presence of multicollinearity: simulation and application of maternal death data. Communications in Statistics: Case Studies, Data Analysis and Applications 2021; 7:394-412. [DOI: 10.1080/23737484.2021.1952493] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
Affiliation(s)
- Talha Omer
- Department of Economics, Finance and Statistics, Jönköping University, Jönköping, Sweden
- Department of Statistics and Computer Science, University of Veterinary and Animal Sciences, Lahore, Pakistan
| | - Pär Sjölander
- Department of Economics, Finance and Statistics, Jönköping University, Jönköping, Sweden
| | - Kristofer Månsson
- Department of Economics, Finance and Statistics, Jönköping University, Jönköping, Sweden
| | - B. M. Golam Kibria
- Department of Mathematics and Statistics, Florida International University, Miami, FL, USA
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Lukman AF, Adewuyi E, Månsson K, Kibria BMG. A new estimator for the multicollinear Poisson regression model: simulation and application. Sci Rep 2021; 11:3732. [PMID: 33580148 PMCID: PMC7881247 DOI: 10.1038/s41598-021-82582-w] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2020] [Accepted: 01/19/2021] [Indexed: 11/26/2022] Open
Abstract
The maximum likelihood estimator (MLE) suffers from the instability problem in the presence of multicollinearity for a Poisson regression model (PRM). In this study, we propose a new estimator with some biasing parameters to estimate the regression coefficients for the PRM when there is multicollinearity problem. Some simulation experiments are conducted to compare the estimators' performance by using the mean squared error (MSE) criterion. For illustration purposes, aircraft damage data has been analyzed. The simulation results and the real-life application evidenced that the proposed estimator performs better than the rest of the estimators.
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Affiliation(s)
- Adewale F Lukman
- Department of Physical Sciences, Landmark University, Omu-Aran, Nigeria.
| | - Emmanuel Adewuyi
- Department of Statistics, Federal University of Technology, Akure, Nigeria
| | - Kristofer Månsson
- Department of Economics, Finance and Statistics, Jönköping University, Jönköping, Sweden
| | - B M Golam Kibria
- Department of Mathematics and Statistics, Florida International University, Miami, USA
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Affiliation(s)
- Muhammad Qasim
- Department of Economics, Finance and Statistics, Jönköping International Business School, Jönköping University, Jönköping, Sweden
| | - Kristofer Månsson
- Department of Economics, Finance and Statistics, Jönköping International Business School, Jönköping University, Jönköping, Sweden
| | - B. M. Golam Kibria
- Department of Mathematics and Statistics, Florida International University, Miami, FL, USA
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Qasim M, Månsson K, Amin M, Golam Kibria BM, Sjölander P. Biased Adjusted Poisson Ridge Estimators-Method and Application. Iran J Sci Technol Trans A Sci 2020; 44:1775-1789. [PMID: 33041601 PMCID: PMC7532743 DOI: 10.1007/s40995-020-00974-5] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/14/2020] [Accepted: 08/31/2020] [Indexed: 10/25/2022]
Abstract
Månsson and Shukur (Econ Model 28:1475-1481, 2011) proposed a Poisson ridge regression estimator (PRRE) to reduce the negative effects of multicollinearity. However, a weakness of the PRRE is its relatively large bias. Therefore, as a remedy, Türkan and Özel (J Appl Stat 43:1892-1905, 2016) examined the performance of almost unbiased ridge estimators for the Poisson regression model. These estimators will not only reduce the consequences of multicollinearity but also decrease the bias of PRRE and thus perform more efficiently. The aim of this paper is twofold. Firstly, to derive the mean square error properties of the Modified Almost Unbiased PRRE (MAUPRRE) and Almost Unbiased PRRE (AUPRRE) and then propose new ridge estimators for MAUPRRE and AUPRRE. Secondly, to compare the performance of the MAUPRRE with the AUPRRE, PRRE and maximum likelihood estimator. Using both simulation study and real-world dataset from the Swedish football league, it is evidenced that one of the proposed, MAUPRRE (k ^ q 4 ) performed better than the rest in the presence of high to strong (0.80-0.99) multicollinearity situation.
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Affiliation(s)
- Muhammad Qasim
- Department of Economics, Finance and Statistics, Jönköping University, Jönköping, Sweden
| | - Kristofer Månsson
- Department of Economics, Finance and Statistics, Jönköping University, Jönköping, Sweden
| | - Muhammad Amin
- Department of Statistics, University of Sargodha, Sargodha, Pakistan
| | - B. M. Golam Kibria
- Department of Mathematics and Statistics, Florida International University, Miami, FL USA
| | - Pär Sjölander
- Department of Economics, Finance and Statistics, Jönköping University, Jönköping, Sweden
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Månsson K, Kibria BMG, Shukur G. A New Liu Type of Estimator for the Restricted SUR Estimator. J Mod Appl Stat Methods 2020. [DOI: 10.22237/jmasm/1556669340] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
Abstract
A new Liu type of estimator for the seemingly unrelated regression (SUR) models is proposed that may be used when estimating the parameters vector in the presence of multicollinearity if the it is suspected to belong to a linear subspace. The dispersion matrices and the mean squared error (MSE) are derived. The new estimator may have a lower MSE than the traditional estimators. It was shown using simulation techniques the new shrinkage estimator outperforms the commonly used estimators in the presence of multicollinearity.
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Abstract
This paper considers the estimation of parameters for the Poisson regression model in the presence of high, but imperfect multicollinearity. To mitigate this problem, we suggest using the Poisson Liu Regression Estimator (PLRE) and propose some new approaches to estimate this shrinkage parameter. The small sample statistical properties of these estimators are systematically scrutinized using Monte Carlo simulations. To evaluate the performance of these estimators, we assess the Mean Square Errors (MSE) and the Mean Absolute Percentage Errors (MAPE). The simulation results clearly illustrate the benefit of the methods of estimating these types of shrinkage parameters in finite samples. Finally, we illustrate the empirical relevance of our newly proposed methods using an empirically relevant application. Thus, in summary, via simulations of empirically relevant parameter values, and by a standard empirical application, it is clearly demonstrated that our technique exhibits more precise estimators, compared to traditional techniques – at least when multicollinearity exist among the regressors.
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Affiliation(s)
- Muhammad Qasim
- Department of Economics, Finance and Statistics, Jönköping University, Jönköping, Sweden
| | - B. M. G. Kibria
- Department of Mathematics and Statistics, Florida International University, Miami, FL, USA
| | - Kristofer Månsson
- Department of Economics, Finance and Statistics, Jönköping University, Jönköping, Sweden
| | - Pär Sjölander
- Department of Economics, Finance and Statistics, Jönköping University, Jönköping, Sweden
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Månsson K, Shukur G, Kibria BMG. Performance of some ridge regression estimators for the multinomial logit model. COMMUN STAT-THEOR M 2018. [DOI: 10.1080/03610926.2013.784996] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Kristofer Månsson
- Department of Economics, Finance and Statistics, Jönköping University, Jönköping, Sweden
| | - Ghazi Shukur
- Department of Economics and Statistics, Centre for Labour Market and Discrimination Studies, LNUC, Linnaeus University, Växjö, Sweden
| | - B. M. Golam Kibria
- Department of Mathematics and Statistics, Florida International University, Miami, Florida, USA
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Sjölander P, Månsson K, Shukur G. Testing for panel cointegration in an error-correction framework with an application to the Fisher hypothesis. COMMUN STAT-SIMUL C 2017. [DOI: 10.1080/03610918.2015.1011332] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Sjölander P, Månsson K, Shukur G. A new nonlinear asymmetric cointegration approach using error correction models. COMMUN STAT-SIMUL C 2017. [DOI: 10.1080/03610918.2014.999087] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Pär Sjölander
- Department of Economics, Finance and Statistics, Jönköping University, Jönköping, Sweden
| | - Kristofer Månsson
- Department of Economics, Finance and Statistics, Jönköping University, Jönköping, Sweden
| | - Ghazi Shukur
- Department of Economics, Finance and Statistics, Jönköping University, Jönköping, Sweden
- Department of Economics and Statistics, Linnaeus University, Växjö, Sweden
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Holgersson HE, Månsson K, Shukur G. Testing for Panel Unit Roots under General Cross-sectional Dependence. COMMUN STAT-SIMUL C 2016. [DOI: 10.1080/03610918.2013.879178] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- H. E.T. Holgersson
- Department of Economics, Finance and Statistics Jönköping, International Business SchoolJönköping, Sweden
- Department of Economics and Statistics, Linnaeus University, Kalmer, Sweden
| | - K. Månsson
- Department of Economics, Finance and Statistics Jönköping, International Business SchoolJönköping, Sweden
- Department of Economics and Statistics, Göteborg University, Göteborg, Sweden
| | - G. Shukur
- Department of Economics, Finance and Statistics Jönköping, International Business SchoolJönköping, Sweden
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Månsson K, Golam Kibria B, Shukur G. A restricted Liu estimator for binary regression models and its application to an applied demand system. J Appl Stat 2015. [DOI: 10.1080/02664763.2015.1092110] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Månsson K, Kibria BMG, Shukur G. Performance of Some Weighted Liu Estimators for Logit Regression Model: An Application to Swedish Accident Data. COMMUN STAT-THEOR M 2014. [DOI: 10.1080/03610926.2012.745562] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Månsson K, Shukur G, Sjölander P. A New Asymmetric Interaction Ridge (AIR) Regression Method. COMMUN STAT-THEOR M 2014. [DOI: 10.1080/03610926.2012.667485] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Kibria BMG, Månsson K, Shukur G. A Simulation Study of Some Biasing Parameters for the Ridge Type Estimation of Poisson Regression. COMMUN STAT-SIMUL C 2014. [DOI: 10.1080/03610918.2013.796981] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Locking H, Månsson K, Shukur G. Performance of Some Ridge Parameters for Probit Regression: With Application to Swedish Job Search Data. COMMUN STAT-SIMUL C 2013. [DOI: 10.1080/03610918.2011.654032] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Månsson K. A Wavelet-Based Approach of Testing for Granger Causality in the Presence of GARCH Effects. COMMUN STAT-THEOR M 2012. [DOI: 10.1080/03610926.2010.529535] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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Månsson K, Shukur G, Golam Kibria BM. A Simulation Study of Some Ridge Regression Estimators under Different Distributional Assumptions. COMMUN STAT-SIMUL C 2010. [DOI: 10.1080/03610918.2010.508862] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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