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Testing in mixed-effects FANOVA models
Institution:1. Department of Statistics & Operations Research, Tel Aviv University, Israel;2. Istituto per le Applicazioni del Calcolo “Mauro Picone”—Sezione di Napoli, Consiglio Nazionale delle Ricerche, Italy;1. School of Mathematics and Statistics, The University of New South Wales, Sydney, NSW 2052, Australia;2. Department of Statistics, George Washington University, Washington, DC 20052, USA;1. Cowles Foundation for Research in Economics, Yale University, Box 208281, New Haven, CT 06520, USA;2. Department of Economics, New York University, 19 West 4th Street, New York, NY 10012, USA
Abstract:We consider the testing problem in the mixed-effects functional analysis of variance models. We develop asymptotically optimal (minimax) testing procedures for testing the significance of functional global trend and the functional fixed effects based on the empirical wavelet coefficients of the data. Wavelet decompositions allow one to characterize various types of assumed smoothness conditions on the response function under the nonparametric alternatives. The distribution of the functional random-effects component is defined in the wavelet domain and captures the sparseness of wavelet representation for a wide variety of functions. The simulation study presented in the paper demonstrates the finite sample properties of the proposed testing procedures. We also applied them to the real data from the physiological experiments.
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