Asymptotics, finite-sample comparisons and applications for two-sample tests with functional data

Journal of Multivariate Analysis - Tập 170 - Trang 202-220 - 2019
Qing Jiang1, Marie Hušková2, Simos G. Meintanis3,4, Lixing Zhu1,5
1School of Statistics, Beijing Normal University, Beijing, P.R. China
2Department of Statistics, Charles University, Prague, Czech Republic
3Department of Economics, National and Kapodistrian University of Athens, Athens, Greece
4Unit for Business Mathematics and Informatics, North-West University, Potchefstroom, South Africa
5Department of Mathematics, Hong Kong Baptist University, Hong Kong

Tài liệu tham khảo

Bárcenas, 2017, Quadratic forms of the empirical processes for the two-sample problem for functional data, Test, 26, 503, 10.1007/s11749-017-0522-x Benko, 2009, Common functional principal components, Ann. Statist., 37, 1, 10.1214/07-AOS516 Berrendero, 2011, Principal components for multivariate functional data, Comput. Statist. Data Anal., 55, 2619, 10.1016/j.csda.2011.03.011 Bilodeau, 2005, A multivariate empirical characteristic function test of independence with normal marginals, J. Multivariate Anal., 95, 345, 10.1016/j.jmva.2004.08.011 Cabaña, 2017, Permutation tests in the two-sample problem for functional data, 77 Cannings, 2017, Random-projection ensemble classification, J. R. Stat. Soc. Ser. B Stat. Methodol., 79, 959, 10.1111/rssb.12228 Chiou, 2014, Linear manifold modeling of multivariate functional data, J. R. Stat. Soc. Ser. B Stat. Methodol., 76, 605, 10.1111/rssb.12038 Chiu, 2009, Generalized Cramér–von Mises goodness-of-fit tests for multivariate distributions, Comput. Statist. Data Anal., 53, 3817, 10.1016/j.csda.2009.04.004 Csörgő, 1986, Testing for normality in arbitrary dimension, Ann. Statist., 14, 708, 10.1214/aos/1176349948 Cuesta-Albertos, 2007, The random projection method in goodness of fit for functional data, Comput. Statist. Data Anal., 51, 4814, 10.1016/j.csda.2006.09.007 Cuevas, 2014, A partial overview of the theory of statistics with functional data, J. Statist. Plann. Inference, 147, 1, 10.1016/j.jspi.2013.04.002 Cuevas, 2004, An ANOVA test for functional data, Comput. Statist. Data Anal., 47, 111, 10.1016/j.csda.2003.10.021 Du, 2014, Testing for serial independence of panel errors, Comput. Statist. Data Anal., 76, 248, 10.1016/j.csda.2013.07.031 Epps, 1993, Characteristic functions and their empirical counterparts: Geometric interpretations and applications to statistical inference, Am. Stat., 47, 33 Febrero-Bande, 2012, Statistical computing in functional data analysis: The R Package fda.usc, J. Stat. Softw., 51, 1, 10.18637/jss.v051.i04 Ferraty, 2006 Fremdt, 2013, Testing the equality of covariance operators in functional samples, Scand. J. Stat., 40, 138, 10.1111/j.1467-9469.2012.00796.x Ghosh, 2016, Distribution-free high-dimensional two-sample tests based on discriminating hyperplanes, Test, 25, 525, 10.1007/s11749-015-0467-x Goia, 2016, Editorial: An introduction to recent advances in high/infinite dimensional statistics, J. Multivariate Anal., 146, 1, 10.1016/j.jmva.2015.12.001 González-Manteiga, 2007, Editorial: Statistics for Functional Data, Comput. Statist. Data Anal., 51, 4788, 10.1016/j.csda.2006.10.017 Gregory, 2015, A two-sample test for equality of means in high dimension, J. Am. Stat. Assoc., 110, 681, 10.1080/01621459.2014.934826 Gretton, 2012, A kernel two-sample test, J. Mach. Learn. Res., 13, 723 Gromenko, 2017, Detection of change in spatiotemporal mean function, J. R. Stat. Soc. Ser. B Stat. Methodol., 79, 29, 10.1111/rssb.12156 Hall, 2002, Permutation tests for equality of distributions in high-dimensional settings, Biometrika, 89, 359, 10.1093/biomet/89.2.359 Hall, 2007, Two-sample tests in functional data analysis starting from discrete data, Statist. Sinica, 17, 1511 Henze, 1997, A new approach to the BHEP tests for multivariate normality, J. Multivariate Anal., 62, 1, 10.1006/jmva.1997.1684 Horváth, 2012 Horváth, 2013, Estimation of the mean of functional time series and a two sample problem, J. R. Stat. Soc. Ser. B Stat. Methodol., 75, 103, 10.1111/j.1467-9868.2012.01032.x Horváth, 2015, Testing equality of means when observations are from functional time series, J. Time Series Anal., 36, 84, 10.1111/jtsa.12095 Hušková, 2008, Tests for the multivariate k-sample problem based on the empirical characteristic function, J. Nonparametr. Stat., 20, 263, 10.1080/10485250801948294 Ibragimov, 1981 Jacques, 2014, Model-based clustering for multivariate functional data, Comput. Statist. Data Anal., 71, 92, 10.1016/j.csda.2012.12.004 Jiang, 2017, Two-sample tests for multivariate functional data, 145 Jiménez-Gamero, 2005, Testing goodness-of-fit for the distribution of errors in multivariate linear models, J. Multivariate Anal., 95, 301, 10.1016/j.jmva.2004.08.010 Kokoszka, 2017, Editorial: Special issue on functional data analysis, ECOSTA, 1, 99 Koutrouvelis, 1980, Regression-type estimation of the parameters of stable laws, J. Amer. Statist. Assoc., 75, 918, 10.1080/01621459.1980.10477573 Kraus, 2012, Dispersion operators and resistant second-order functional data analysis, Biometrika, 99, 813, 10.1093/biomet/ass037 Lindsay, 2014, Kernels, degrees of freedom and power properties of quadratic distance goodness-of-fit tests, J. Amer. Statist. Assoc., 109, 395, 10.1080/01621459.2013.836972 Nieto-Reyes, 2014, A random projection based test of Gaussianity for stationary processes, Comput. Statist. Data Anal., 75, 124, 10.1016/j.csda.2014.01.013 Panaretos, 2010, Second-order comparison of Gaussian random functions and the geometry of DNA minicircles, J. Amer. Statist. Assoc., 105, 670, 10.1198/jasa.2010.tm09239 Pini, 2017, Interval-wise testing for functional data, J. Nonparametr. Stat., 29, 407, 10.1080/10485252.2017.1306627 Pomann, 2016, two-sample hypothesis testing for functional data with application to a diffusion tensor imaging study of multiple sclerosis, J. R. Stat. Soc. Ser. C. Appl. Stat., 65, 395, 10.1111/rssc.12130 Pudelko, 2005, On a new affine invariant and consistent test for multivariate normality, Probab. Math. Statist., 25, 43 Ramsay, 2005 Ruiz-Meana, 2003, Cariporide preserves mitochondrial proton gradient and delays ATP depletion in cardiomyocytes during ischemic conditions, Amr. J. Physiol. Heart Circ. Physiol., 285, H999, 10.1152/ajpheart.00035.2003 Shao, 2010, A characterization of multivariate normality through univariate projections, J. Multivariate Anal., 101, 2637, 10.1016/j.jmva.2010.04.015 Székely, 2005, Hierarchical clustering via joint between-within distances: Extending Ward’s minimum variance method, J. Classification, 22, 151, 10.1007/s00357-005-0012-9 Székely, 2013, Energy statistics: A class of statistics based on distances, J. Statist. Plann. Inference, 143, 249, 10.1016/j.jspi.2013.03.018 Tenreiro, 2009, On the choice of the smoothing parameter for the BHEP goodness-of-fit test, Comput. Statist. Data Anal., 53, 1038, 10.1016/j.csda.2008.09.002 Valderama, 2007, An overview to modelling functional data, Comput. Statist., 22, 331, 10.1007/s00180-007-0043-2 Wang, 2016, Functional data analysis, Ann. Rev. Stat. Appl., 3, 257, 10.1146/annurev-statistics-041715-033624 Welsh, 1986, Implementing empirical characteristic function procedures, Statist. Probab. Lett., 4, 65, 10.1016/0167-7152(86)90019-2 Zhang, 2010, Two-sample tests for functional data, Comm. Statist. Theory Methods, 39, 559, 10.1080/03610920902755839 Zhang, 2015, Two sample inference for the second-order property of temporally dependent functional data, Bernoulli, 21, 909, 10.3150/13-BEJ592