Wavelet Functional Data Analysis for FANOVA Models under Dependent Errors

TL;DR

This paper extends wavelet-based FANOVA testing methods to models with dependent errors, introducing an iterative estimation procedure and demonstrating its effectiveness through real and simulated data analyses.

Contribution

It develops a novel wavelet functional data analysis approach for FANOVA models with dependent errors, including an iterative estimation method and nonparametric tests.

Findings

Effective in real data applications

Performs well under realistic sample sizes

Improves upon existing iid error methods

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.