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Title: Two-sample tests for relevant differences in the eigenfunctions of covariance operators Authors:  Alexander Aue - UC Davis (United States) [presenting]
Holger Dette - Ruhr-Universitaet Bochum (Germany)
Gregory Rice - University of Waterloo (Canada)
Abstract: Two-sample tests for functional time series data are considered. These tests have become widely available in conjunction with the advent of modern complex observation systems. Particular interest is in finding out whether two sets of independent functional time-series observations share the shape of their primary modes of variation as encoded by the eigenfunctions of the respective covariance operators. To this end, a novel testing approach is introduced that connects with, and extends, existing literature in two main ways. First, tests are set up in the relevant testing framework, where interest is not in testing an exact null hypothesis but rather in detecting deviations deemed sufficiently significant, with significance often determined in consultation with scientific guidelines. Second, the proposed test statistics rely on a self-normalization principle that helps avoid the notoriously difficult task of estimating the long-run covariance structure of the underlying functional time series. The main theoretical result to be discussed is the derivation of the large-sample behavior of the proposed test statistics. Empirical evidence, indicating that the proposed procedures work well in finite samples, is provided through a simulation study, also comparing with competing methods and an application to annual temperature data.