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

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.

This article is part of a Festschrift in honor of Marie Hušková (title of the Festschrift: Asymptotic and Methodological Statistics)