A review of goodness-of-fit tests for models involving functional data

TL;DR

This paper reviews recent goodness-of-fit tests for functional data models, summarizing developments over the past decade within the i.i.d. framework for distribution and regression models.

Contribution

It provides a comprehensive and compact review of existing goodness-of-fit tests for models with functional data, covering both distribution and regression contexts.

Findings

Summarizes key goodness-of-fit tests for functional data models

Highlights methodological advances over the last decade

Provides a unified framework within the i.i.d. setting

Abstract

A sizable amount of goodness-of-fit tests involving functional data have appeared in the last decade. We provide a relatively compact revision of most of these contributions, within the independent and identically distributed framework, by reviewing goodness-of-fit tests for distribution and regression models with functional predictor and either scalar or functional response.