Principal component-based adaptive Neyman test for functional data

Abstract

Functional data consist of a group of functions as their a??observationsa??. Study of functional data is an active topic of current statistical research. The adaptive Neyman test (ANT) has been proposed for high-dimensional testing problems and shown to be more powerful than some existing distribution-based tests. It has been successfully applied to nonparametric rank tests, especially to some hypothesis testing problems for curve data corrupted with a white noise or stationary errors. In functional data analysis, many curve data may not result from a white noise or stationary errors, rather the underlying process may be highly correlated or nonstationary. In our study, we attempt to extend the ANT for such functional data. Our strategy is to apply the ANT directly to the normalized principal components scores of functional data, resulting in the so-called PC-based ANT. Simulation studies are conducted to examine the proposed test. It is illustrated by a real functional data example.