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Long AS, Reich BJ, Staicu AM, Meitzen J. A nonparametric test of group distributional differences for hierarchically clustered functional data. Biometrics 2023; 79:3778-3791. [PMID: 36805970 PMCID: PMC10695330 DOI: 10.1111/biom.13846] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2022] [Accepted: 02/03/2023] [Indexed: 02/22/2023]
Abstract
Biological sex and gender are critical variables in biomedical research, but are complicated by the presence of sex-specific natural hormone cycles, such as the estrous cycle in female rodents, typically divided into phases. A common feature of these cycles are fluctuating hormone levels that induce sex differences in many behaviors controlled by the electrophysiology of neurons, such as neuronal membrane potential in response to electrical stimulus, typically summarized using a priori defined metrics. In this paper, we propose a method to test for differences in the electrophysiological properties across estrous cycle phase without first defining a metric of interest. We do this by modeling membrane potential data in the frequency domain as realizations of a bivariate process, also depending on the electrical stimulus, by adopting existing methods for longitudinal functional data. We are then able to extract the main features of the bivariate signals through a set of basis function coefficients. We use these coefficients for testing, adapting methods for multivariate data to account for an induced hierarchical structure that is a product of the experimental design. We illustrate the performance of the proposed approach in simulations and then apply the method to experimental data.
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Affiliation(s)
- Alexander S Long
- Department of Statistics, North Carolina State University, Raleigh, North Carolina, U.S.A
| | - Brian J Reich
- Department of Statistics, North Carolina State University, Raleigh, North Carolina, U.S.A
| | - Ana-Maria Staicu
- Department of Statistics, North Carolina State University, Raleigh, North Carolina, U.S.A
| | - John Meitzen
- Department of Biological Sciences, North Carolina State University, Raleigh, North Carolina, U.S.A
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2
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Ramsay K, Chenouri S. Robust nonparametric hypothesis tests for differences in the covariance structure of functional data. CAN J STAT 2023. [DOI: 10.1002/cjs.11767] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/28/2023]
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3
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Yamaguchi H, Murakami H. Interpoint distance-based two-sample tests for functional data. COMMUN STAT-THEOR M 2022. [DOI: 10.1080/03610926.2022.2148475] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
Affiliation(s)
- Hikaru Yamaguchi
- 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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van Delft A, Dette H. Pivotal tests for relevant differences in the second order dynamics of functional time series. BERNOULLI 2022. [DOI: 10.3150/21-bej1418] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Anne van Delft
- Department of Statistics, Columbia University, 1255 Amsterdam Avenue, New York, NY 10027, USA
| | - Holger Dette
- Ruhr-Universität Bochum, Fakultät für Mathematik, 44780 Bochum, Germany
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Balogoun ASK, Nkiet GM, Ogouyandjou C. Kernel based method for the k-sample problem with functional data. COMMUN STAT-THEOR M 2022. [DOI: 10.1080/03610926.2020.1849719] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Armando S. K. Balogoun
- Institut de Mathématiques et de Sciences Physiques, Département de Mathématiques, Porto Novo, Bénin
| | - Guy M. Nkiet
- Université des Sciences et Techniques de Masuku, Département de Mathématiques et Informatique, Franceville, Gabon
| | - Carlos Ogouyandjou
- Institut de Mathématiques et de Sciences Physiques, Département de Mathématiques, Porto Novo, Bénin
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Minh HQ. Entropic Regularization of Wasserstein Distance Between Infinite-Dimensional Gaussian Measures and Gaussian Processes. J THEOR PROBAB 2022. [DOI: 10.1007/s10959-022-01165-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Detecting relevant differences in the covariance operators of functional time series: a sup-norm approach. ANN I STAT MATH 2021. [DOI: 10.1007/s10463-021-00795-2] [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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Bissantz K, Bissantz N, Proksch K. Nonparametric detection of changes over time in image data from fluorescence microscopy of living cells. Scand Stat Theory Appl 2021. [DOI: 10.1111/sjos.12517] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Affiliation(s)
- Kathrin Bissantz
- Bundesanstalt für Arbeitsschutz und Arbeitsmedizin (BAuA) Dortmund Germany
| | | | - Katharina Proksch
- Mathematics and Computer Science (EEMCS) University of Twente Faculty of Electrical Engineering NB Enschede The Netherlands
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10
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Asymptotic normality of a generalized maximum mean discrepancy estimator. Stat Probab Lett 2021. [DOI: 10.1016/j.spl.2020.108961] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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11
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Affiliation(s)
- Olimjon Sh. Sharipov
- Institut for Mathematical Stochastics, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany
| | - Martin Wendler
- Institut for Mathematical Stochastics, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany
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Dette H, Kokot K, Volgushev S. Testing relevant hypotheses in functional time series via self-normalization. J R Stat Soc Series B Stat Methodol 2020. [DOI: 10.1111/rssb.12370] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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13
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Affiliation(s)
- Tomasz Górecki
- Faculty of Mathematics and Computer Science Adam Mickiewicz University Poznań 61‐614 Poland
| | - Lajos Horváth
- Department of Mathematics University of Utah Salt Lake City UT 84112‐0090 USA
| | - Piotr Kokoszka
- Department of Statistics Colorado State University Fort Collins CO 80523-1877 USA
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Guo J, Zhou B, Chen J, Zhang JT. An $${{\varvec{L}}}^{2}$$L2-norm-based test for equality of several covariance functions: a further study. TEST-SPAIN 2019. [DOI: 10.1007/s11749-018-0617-z] [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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15
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Zhang T, Wang Z, Wan Y. Functional test for high-dimensional covariance matrix, with application to mitochondrial calcium concentration. Stat Pap (Berl) 2019. [DOI: 10.1007/s00362-019-01133-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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16
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Chiou JM, Chen YT, Hsing T. Identifying multiple changes for a functional data sequence with application to freeway traffic segmentation. Ann Appl Stat 2019. [DOI: 10.1214/19-aoas1242] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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18
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Zhang JT, Cheng MY, Wu HT, Zhou B. A new test for functional one-way ANOVA with applications to ischemic heart screening. Comput Stat Data Anal 2019. [DOI: 10.1016/j.csda.2018.05.004] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
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19
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Boente G, Rodriguez D, Sued M. The spatial sign covariance operator: Asymptotic results and applications. J MULTIVARIATE ANAL 2019. [DOI: 10.1016/j.jmva.2018.10.002] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Asymptotics, finite-sample comparisons and applications for two-sample tests with functional data. J MULTIVARIATE ANAL 2019. [DOI: 10.1016/j.jmva.2018.09.002] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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21
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Procrustes Metrics on Covariance Operators and Optimal Transportation of Gaussian Processes. SANKHYA A 2019. [DOI: 10.1007/s13171-018-0130-1] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
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22
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Guo J, Zhou B, Zhang JT. New Tests for Equality of Several Covariance Functions for Functional Data. J Am Stat Assoc 2018. [DOI: 10.1080/01621459.2018.1483827] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
Affiliation(s)
- Jia Guo
- College of Economics and Management, Zhejiang University of Technology, Hangzhou, China
- ACEMS and School of Mathematics and Statistics, University of Melbourne, Melbourne, Parkville VIC, Australia
| | - Bu Zhou
- School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, China
| | - Jin-Ting Zhang
- Department of Statistics and Applied Probability, National University of Singapore, Singapore
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23
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Guo J, Zhou B, Zhang JT. Testing the equality of several covariance functions for functional data: A supremum-norm based test. Comput Stat Data Anal 2018. [DOI: 10.1016/j.csda.2018.02.002] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Kokoszka P, Miao H, Zheng B. Testing for asymmetry in betas of cumulative returns: Impact of the financial crisis and crude oil price. STATISTICS & RISK MODELING 2017. [DOI: 10.1515/strm-2016-0010] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Abstract
We introduce a functional factor model to investigate the dependence of cumulative return curves of individual assets on the market and other factors.
We propose a new statistical test to determine whether the dependence in two sample periods are equal.
The statistical properties of the test are established by asymptotic theory and simulations.
We apply this test to study the impact of the recent financial crisis and trends in oil price on individual stock and sector ETFs.
Our analysis reveals the significance of the daily oil futures curves and their different impact on individual stocks and sector ETFs.
It also shows that the functional approach has an information content different from that obtained from scalar factor models for point-to-point returns.
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Affiliation(s)
- Piotr Kokoszka
- Department of Statistics , Colorado State University , Fort Collins , USA
| | - Hong Miao
- Department of Finance and Real Estate , Colorado State University , Fort Collins , USA
| | - Ben Zheng
- Department of Statistics , Colorado State University , Fort Collins , USA
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Tavakoli S, Panaretos VM. Detecting and Localizing Differences in Functional Time Series Dynamics: A Case Study in Molecular Biophysics. J Am Stat Assoc 2016. [DOI: 10.1080/01621459.2016.1147355] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Shahin Tavakoli
- Statistical Laboratory, University of Cambridge, Cambridge, UK
| | - Victor M. Panaretos
- Institut de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
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29
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On two sample inference for eigenspaces in functional data analysis with dependent errors. J Stat Plan Inference 2016. [DOI: 10.1016/j.jspi.2016.02.001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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30
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Pomann GM, Staicu AM, Ghosh S. A Two Sample Distribution-Free Test for Functional Data with Application to a Diffusion Tensor Imaging Study of Multiple Sclerosis. J R Stat Soc Ser C Appl Stat 2016; 65:395-414. [PMID: 27041772 DOI: 10.1111/rssc.12130] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
Motivated by an imaging study, this paper develops a nonparametric testing procedure for testing the null hypothesis that two samples of curves observed at discrete grids and with noise have the same underlying distribution. The objective is to formally compare white matter tract profiles between healthy individuals and multiple sclerosis patients, as assessed by conventional diffusion tensor imaging measures. We propose to decompose the curves using functional principal component analysis of a mixture process, which we refer to as marginal functional principal component analysis. This approach reduces the dimension of the testing problem in a way that enables the use of traditional nonparametric univariate testing procedures. The procedure is computationally efficient and accommodates different sampling designs. Numerical studies are presented to validate the size and power properties of the test in many realistic scenarios. In these cases, the proposed test has been found to be more powerful than its primary competitor. Application to the diffusion tensor imaging data reveals that all the tracts studied are associated with multiple sclerosis and the choice of the diffusion tensor image measurement is important when assessing axonal disruption.
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Affiliation(s)
| | | | - Sujit Ghosh
- North Carolina State University, Raleigh and Statistical and Applied Mathematical Sciences Institute, RTP, NC. USA
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33
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Zhang X, Shao X. Two sample inference for the second-order property of temporally dependent functional data. BERNOULLI 2015. [DOI: 10.3150/13-bej592] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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34
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Pigoli D, Aston JAD, Dryden IL, Secchi P. Distances and inference for covariance operators. Biometrika 2014. [DOI: 10.1093/biomet/asu008] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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