Interpoint distance-based two-sample tests for functional data

References

• Araujo, A., and E. Giné. 1980. The central limit theorem for real and Banach valued random variables. New York: John Wiley & Sons.
   Google Scholar
• Bakshaev, A. 2009. Goodness of fit and homogeneity tests on the basis of N-distances. Journal of Statistical Planning and Inference 139 (11):3750–8. doi:10.1016/j.jspi.2009.05.014.
   Web of Science ®Google Scholar
• Baringhaus, L., and C. Franz. 2004. On a new multivariate two-sample test. Journal of Multivariate Analysis 88 (1):190–206. doi:10.1016/S0047-259X(03)00079-4.
   Web of Science ®Google Scholar
• Biswas, M., and A. K. Ghosh. 2014. A nonparametric two-sample test applicable to high dimensional data. Journal of Multivariate Analysis 123:160–71. doi:10.1016/j.jmva.2013.09.004.
   Web of Science ®Google Scholar
• Benko, M., W. Härdle, and A. Kneip. 2009. Common functional principal components. The Annals of Statistics 37 (1):1–34. doi:10.1214/07-AOS516.
   Web of Science ®Google Scholar
• Borwein, J. M., and J. D. Vanderwerff. 2010. Convex Functions: Constructions, Characterizations and Counterexamples (Encyclopedia of Mathematics and its Applications). Cambridge: Cambridge University Press.
   Google Scholar
• Brunner, E., A. C. Bathke, and F. Konietschke. 2019. Rank and Pseudo-Rank Procedures for Independent Observations in Factorial Designs: Using R and SAS. Heidelberg: Springer.
   Google Scholar
• Chakraborty, A., and P. Chaudhuri. 2015. A Wilcoxon–Mann–Whitney-type test for infinite-dimensional data. Biometrika 102 (1):239–46. doi:10.1093/biomet/asu072.
   Web of Science ®Google Scholar
• Crainiceanu, C. M., A. M. Staicu, and C.-Z. Di. 2009. Generalized multilevel functional regression. Journal of the American Statistical Association 104 (488):1550–61. doi:10.1198/jasa.2009.tm08564.
   PubMed Web of Science ®Google Scholar
• Di, C.-Z., C. M. Crainiceanu, B. S. Caffo, and N. M. Punjabi. 2009. Multilevel functional principal component analysis. The Annals of Applied Statistics 3 (1):458–88. doi:10.1214/08-AOAS206.
   PubMed Web of Science ®Google Scholar
• Efron, B., and C. Stein. 1981. The jackknife estimate of variance. The Annals of Statistics 9 (3):586–96. doi:10.1214/aos/1176345462.
   Web of Science ®Google Scholar
• Ferraty, F., and P. Vieu. 2006. Nonparametric functional data analysis: Theory and practice. New York: Springer-Verlag.
   Google Scholar
• Ferraty, F., P. Vieu, and S. Viguier-Pla. 2007. Factor-based comparison of groups of curves. Computational Statistics & Data Analysis 51 (10):4903–10. doi:10.1016/j.csda.2006.10.001.
   Web of Science ®Google Scholar
• Fremdt, S., L. Horvath, P. Kokoszka, and J. Steinebach. 2013. Testing the equality of covariance operators in functional samples. Scandinavian Journal of Statistics 40 (1):138–52. doi:10.1111/j.1467-9469.2012.00796.x.
   Web of Science ®Google Scholar
• Goldsmith, J., C. M. Crainiceanu, B. Caffo, and D. Reich. 2012. Longitudinal penalized functional regression for cognitive outcomes on neuronal tract measurements. Journal of the Royal Statistical Society. Series C, Applied Statistics 61 (3):453–69. doi:10.1111/j.1467-9876.2011.01031.x.
   PubMedGoogle Scholar
• Hall, P., and I. Van Keilegom. 2007. Two-sample tests in functional data analysis starting from discrete data. Statistica Sinica 17 (4):1511–31.
   Web of Science ®Google Scholar
• Horváth, L., P. Kokoszka, and R. Reeder. 2013. Estimation of the mean of functional time series and a two-sample problem. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 75 (1):103–22. doi:10.1111/j.1467-9868.2012.01032.x.
   Web of Science ®Google Scholar
• Klebanov, L. B. 2005. N-Distances and Their Applications. Prague: Karolinum.
   Google Scholar
• Kraus, D., and V. Panaretos. 2012. Dispersion operators and resistant second-order analysis of functional data. Biometrika 99 (4):813–32. doi:10.1093/biomet/ass037.
   Web of Science ®Google Scholar
• Lee, A. J. 1990. U-Statistics: Theory and Practice. New York: Marcel Dekker.
   Google Scholar
• Pettitt, A. N. 1976. A two-sample Anderson–Darling rank statistic. Biometrika 63 (1):161–8. doi:10.1093/biomet/63.1.161.
   Web of Science ®Google Scholar
• Pomann, G.-M., A.-M. Staicu, and S. Ghosh. 2016. 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 65 (3):395–414. doi:10.1111/rssc.12130.
   PubMed Web of Science ®Google Scholar
• Ramsay, J. O., and B. W. Silverman. 2005. Functional Data Analysis. New York: Springer.
   Google Scholar
• Székely, G. J., and M. L. Rizzo. 2013. Energy statistics: A class of statistics based on distances. Journal of Statistical Planning and Inference 143 (8):1249–72. doi:10.1016/j.jspi.2013.03.018.
   Web of Science ®Google Scholar
• Yao, F., H.-G. Müller, and J.-L. Wang. 2005. Functional data analysis for sparse longitudinal data. Journal of the American Statistical Association 100 (470):577–90. doi:10.1198/016214504000001745.
   Web of Science ®Google Scholar
• Zhang, J.-T., X. Liang, and S. Xiao. 2010. On the two-sample Behrens–Fisher problem for functional data. Journal of Statistical Theory and Practice 4 (4):571–87. doi:10.1080/15598608.2010.10412005.
   Google Scholar