A two-sample distribution-free test for functional data with application to a diffusion tensor imaging study of multiple sclerosis

Journal of the Royal Statistical Society. Series C: Applied Statistics

Volumn 65, Issue 3, 2016, Pages 395-414

  Pomann, Gina Maria ^a   Staicu, Ana Maria ^b   Ghosh, Sujit ^b,c  

^a DUKE UNIVERSITY   (United States)

^b NORTH CAROLINA STATE UNIVERSITY   (United States)

^c Statistical and Applied Mathematical Sciences Institute USA   (United States)

Author keywords

Diffusion tensor imaging; Functional principal component analysis; Hypothesis testing; Multiple sclerosis

Indexed keywords

EID: 84959105170     PISSN: 00359254     EISSN: 14679876     Source Type: Journal    
DOI: 10.1111/rssc.12130     Document Type: Article

References (48)

1. Aslan, B. and Zech, G. (2005) New test for the multivariate two-sample problem based on the concept of minimum energy. J. Statist. Computn Simuln, 75, 109-119
2. Benko, M., Hardle, W. and Kneip, A. (2009) Common functional principal components. Ann. Statist., 37, 1-34
3. Bohm, G. and Zech, G. (2010) Introduction to Statistics and Data Analysis for Physicists. Deutsches Elektronen-Synchrotron
4. Bosq, D. (2000) Linear Processes in Function Spaces: Theory and Applications. New York: Springer
5. Corain, L., Melas, V. B., Pepelyshev, A. and Salmaso, L. (2014) New insights on permutation approach for hypothesis testing on functional data. Adv. Data Anal. Classificn, 8, 339-356
6. Crainiceanu, C., Reiss, P., Goldsmith, J., Huang, L., Huo, L., Scheipl, F., Greven, S., Harezlak, J., Kundu, M. G. and Zhao, Y. (2012) refund: regression with functional data. R Package Version 0.1-6.http://cran.rproject.org/package=refund
7. Cuevas, A., Febrero, M. and Fraiman, R. (2004) An anova test for functional data. Computnl Statist. Data Anal., 47, 111-122
8. Di, C., Crainiceanu, C. M., Caffo, B. S. and Punjabi, N. M. (2009) Multilevel functional principal component analysis. Ann. Appl. Statist., 3, 458-488
9. Dorris, D. M., Cao, J., Willett, J. A., Hauser, C. A. and Meitzen, J. (2014) Intrinsic excitability varies by sex in prepubertal striatal medium spiny neurons. J. Neurphysiol., 113, 720-729
10. Estévez-Pérez, G. and Vilar, J. A. (2008) Functional anova starting from discrete data: an application to air quality data. Environ. Ecol. Statist., 20, 495-515
11. Evangelou, N., Konz, D., Esiri, M., Smith, S., Palace, J. and Matthews, P. (2000) Regional axonal loss in the corpus callosum correlates with cerebral white matter lesion volume and distribution in multiple sclerosis. Brain, 123, 1845-1849
12. Ferraty, F., Vieu, P. and Viguier-Pla, S. (2007) Factor-based comparison of groups of curves. Computnl Statist. Data Anal., 51, 4903-4910
13. Fremdt, S., Horvath, L., Kokoszka, P. and Steinebach, J. (2012) Testing the equality of covariance operators in functional samples. Scand. J. Statist., 40, 138-152
14. Friedman, J. and Rafsky, L. (1979) Multivariate generalizations of the Wald-Wolfowitz and Smirnov two-sample tests. Ann. Statist., 7, 697-717
15. Gertheiss, J., Goldsmith, J., Crainiceanu, C. and Greven, S. (2013a) Longitudinal scalar-on-functions regression with application to tractography data. Biostatistics, 14, 447-461
16. Gertheiss, J., Maity, A. and Staicu, A.-M. (2013b) Variable selection in generalized functional linear models. Stat, 2, 86-101
17. Goldsmith, J., Bobb, J., Crainiceanu, C., Caffo, B. and Reich, D. (2011) Penalized functional regression. J. Computnl Graph. Statist., 20, 850-851
18. Goldsmith, J., Crainiceanu, C. M., Caffo, B. and Reich, D. (2012) Longitudinal penalized functional regression for cognitive outcomes on neuronal tract measurements. Appl. Statist., 61, 453-469
19. Greven, S., Crainiceanu, C. M., Caffo, B. S. and Reich, D. (2010) Longitudinal functional principal component analysis. Electron. J. Statist., 4, 1022-1054
20. Hall, P., Muller, H.-G. and Wang, J.-L. (2006) Properties of principal component methods for functional and longitudinal data analysis. Ann. Statist., 34, 1493-1517
21. Hall, P. and Van Keilegom, I. (2007) Two-sample tests in functional data analysis starting from discrete data. Statist. Sin., 17, 1511-1531
22. Horváth, L., Kokoszka, P. and Reeder, R. (2013) Estimation of the mean of functional time series and a two-sample problem. J. R. Statist. Soc. B, 75, 103-122
23. Ivanescu, A. E., Staicu, A.-M., Scheipl, F. and Greven, S. (2015) Penalized function-function regression. Computnl Statist., 30, 539-568
24. Kraus, D. and Panaretos, V. (2012) Dispersion operators and resistant second-order analysis of functional data. Biometrika, 99, 813-832
25. Laukaitis, A. and Račkauskas, A. (2005) Functional data analysis for clients segmentation tasks. Eur. J. Oper. Res., 163, 210-216
26. Li, M., Staicu, A.-M. and Bondell, H. D. (2014) Incorporating covariates in skewed functional data models. Biostatistics, 16, 413-426
27. Massey, Jr, F. (1951) The Kolmogorov-Smirnov test for goodness of fit. J. Am. Statist. Ass., 46, 68-78
28. McLean, M. W., Hooker, G., Staicu, A.-M., Scheipl, F. and Ruppert, D. (2014) Functional generalized additive models. J. Computnl Graph. Statist., 23, 249-269
29. Möller, A., Tutz, G. and Gertheiss, J. (2014) Random forests for functional covariates. In Proc. 29th Int. Wrkshp Statistical Modelling (eds T. Kneib, F. Sobotka, J. Fahrenholz and H. Irmer), pp. 219-223
30. Ozturk, A., Smith, S., Gordon-Lipkin, E., Harrison, D., Shiee, N., Pham, D., Caffo, B., Calabresi, P. and Reich, D. (2010) Mri of the corpus callosum in multiple sclerosis: association with disability. Mult. Scler., 16, 166-177
31. Pettitt, A. N. (1976) A two-sample Anderson-Darling rank statistic. Biometrika, 63, 161-168
32. Ramsay, J. and Silverman, B. (2005) Functional Data Analysis. New York: Springer
33. R Core Team (2015) R: a Language and Environment for Statistical Computing. Vienna: R Foundation for Statistical Computing
34. Read, T. and Cressie, N. (1988) Goodness-of-fit Statistics for Discrete Multivariate Data. New York: Springer
35. Reich, D. S., Ozturk, A., Calabresi, P. A. and Mori, S. (2010) Automated vs. conventional tractography in multiple sclerosis: variability and correlation with disability. Neuroimage, 49, 3047-3056
36. Schilling, M. (1986) Multivariate two-sample tests based on nearest neighbors. J. Am. Statist. Ass., 81, 799-806
37. Scholz, F. (2011) Anderson-Darling K-sample test and combinations of such tests. R Package adk.University of Washington, Seattle. (Available fromhttps://cran.rproject.org/src/contrib/Archive/adk/
38. Scholz, F. and Stephens, M. (1987) K-sample Anderson-Darling tests. J. Am. Statist. Ass., 82, 918-924
39. Staicu, A.-M., Crainiceanu, C. M. and Carroll, R. J. (2010) Fast methods for spatially correlated multilevel functional data. Biostatistics, 11, 177-194
40. Staicu, A.-M., Crainiceanu, C. M., Reich, D. S. and Ruppert, D. (2012) Modeling functional data with spatially heterogeneous shape characteristics. Biometrics, 68, 331-343
41. Staicu, A.-M., Li, Y., Crainiceanu, C. M. and Ruppert, D. (2014) Likelihood ratio tests for dependent data with applications to longitudinal and functional data analysis. Scand. J. Statist., 41, 932-949
42. Staniswalis, J. G. and Lee, J. J. (1998) Nonparametric regression analysis of longitudinal data. J. Am. Statist. Ass., 93, 1403-1418
43. Stephens, M. A. (1974) Edf statistics for goodness of fit and some comparisons. J. Am. Statist. Ass., 69, 730-737
44. Wei, L. and Lachin, J. (1984) Two-sample asymptotically distribution-free tests for incomplete multivariate observations. J. Am. Statist. Ass., 79, 653-661
45. Wurtz, D., Chalabi, Y. and Luksan, L. (2006) Parameter estimation of arma models with garch/aparch errors an r and splus software implementation. University of Pennsylvania, Philadelphia
46. Yao, F., Muller, H. and Wang, J. (2005) Functional data analysis for sparse longitudinal data. J. Am. Statist. Ass., 100, 577-591
47. Zhang, J.-T. and Chen, J. (2007) Statistical inferences for functional data. Ann. Statist., 35, 1052-1079
48. Zhang, J.-T., Liang, X. and Xiao, S. (2010) On the two-sample Behrens-Fisher problem for functional data. J. Statist. Theor. Pract., 4, 571-587