Title: New tests for equality of several covariance functions for functional data
Authors: Jin-Ting Zhang - National University of Singapore (Singapore) [presenting]
Abstract: Two new tests for the equality of the covariance functions of several functional populations are discussed, namely a quasi GPF test and a quasi Fmax test. Unlike several existing tests, they are scale-invariant in the sense that their test statistics will not change if we multiply each of the observed functions by any non-zero function of time. We derive the asymptotic random expressions of the two tests under the null hypothesis and show that under some mild conditions, the asymptotic null distribution of the quasi GPF test is a chi-squared-type mixture whose distribution can be well approximated by a simple scaled chi-squared distribution. We also describe a random permutation method for approximating the null distributions of the quasi GPF and Fmax tests. Simulation studies are presented to demonstrate the finite-sample performance of the new tests against five existing tests. An illustrative example is also presented.