Wavelet Functional Data Analysis for FANOVA Models under Dependent Errors

Abstract

We extend the wavelet tests for fixed effects FANOVA models with iid errors, proposed in Abramovich et al, 2004 to FANOVA models with dependent errors and provide an iterative Cochrane-Orcutt type procedure to estimate the parameters and the functional. The function is estimated through a nonlinear wavelet estimator. Nonparametric tests based on the optimal performance of nonlinear wavelet estimators are also proposed. The method is illustrated on real data sets and in simulated studies. The simulation also addresses the test performance under realistic sample sizes.