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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, namely a quasi GPF test and a quasi Fmax test, are obtained via Globalizing a Point-wise quasi F-test statistic with integration and taking its supremum over some time interval of interest, respectively. Unlike several existing tests, they are scale-invariant. The asymptotic random expressions of the two tests under the null hypothesis and a local alternative are derived. It is showed 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 propose 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.