Quadratic forms of the empirical processes for the two sample problem for functional data

TL;DR

This paper develops quadratic form-based statistical methods for two-sample testing in functional data analysis, establishing their convergence to Gaussian limits under certain conditions and demonstrating their practical applicability.

Contribution

It introduces a new approach using quadratic forms of the empirical process for two-sample tests in functional data, with proven convergence properties.

Findings

Convergence of the proposed statistics to Gaussian limits.

Method demonstrated effective in practical examples.

Applicable under metric entropy conditions for smooth data.

Abstract

The use of quadratic forms of the empirical process for the two-sample problem in the context of functional data is considered. The convergence of the family of statistics proposed to a Gaussian limit is established under metric entropy conditions for smooth functional data. The applicability of the proposed methodology is evaluated in examples.