TESTING THE EQUALITY OF SEVERAL COVARIANCE FUNCTIONS FOR FUNCTIONAL DATA

Abstract

In functional data analysis, one-way ANOVA problems have been studied by many researchers in recent decades. And the equal-covariance assumption is commonly assumed in these equal-mean function testing problems. So it is of interest to check whether this assumption holds or not. In this thesis, we discuss three types of methods, i.e., the L2-norm based test, the supremum-norm based test and the quasi F-type tests, for the multi-sample equal-covariance function testing problem. The asymptotic null distributions of the tests are derived and methods based on Welch-Satterthwaite moment-matching or random permutation are proposed to approximate the null distributions. The asymptotic powers are also investigated and all the tests are shown to be root-n consistent. Intensive simulation studies are conducted to compare the proposed tests with other existing tests numerically and to demonstrate the finite sample performance of the proposed tests. Some real data applications are also presented to illustrate the proposed methods.