Goodness-of-fit testing for the error distribution in functional linear models

TL;DR

This paper develops goodness-of-fit tests for the error distribution in functional linear models, focusing on normality testing, using asymptotic expansions of empirical distribution and characteristic functions based on residuals.

Contribution

It introduces new asymptotic expansions and testing procedures for the error distribution in functional linear models, including tests for normality.

Findings

Asymptotic expansions derived for empirical distribution and characteristic functions.

New goodness-of-fit tests for error distribution in functional linear models.

Application to normality testing of residuals.

Abstract

We consider the error distribution in functional linear models with scalar response and functional covariate. Different asymptotic expansions of the empirical distribution function and the empirical characteristic function based on estimated residuals under different model assumptions are discussed. The results are applied for simple and composite goodness-of-fit testing for the error distribution, in particular testing for normal distribution.