Testing the Missing Completely at Random Assumption for Functional Data

TL;DR

This paper develops statistical tests to verify if functional data observed on subsets of their domain are missing completely at random, a crucial assumption for many analysis methods, filling a significant gap in the field.

Contribution

The paper introduces a novel testing framework for the MCAR assumption in functional data, including deterministic and data-driven clustering approaches, with asymptotic validation.

Findings

Tests effectively distinguish MCAR from non-MCAR missing patterns.

Framework validated through real data applications.

Asymptotic properties established for the proposed tests.

Abstract

We consider functional data which have only been observed on a subset of their domain. This paper aims to develop statistical tests to determine whether the function and the domain over which it is observed are independent. The assumption that data is missing completely at random (MCAR) is essential for many functional data methods handling incomplete observations. However, no general testing procedures have been established to validate this assumption. We address this critical gap by introducing a testing framework which is generally based on a partition of the observation patterns. Besides deterministic partitions, we also consider a data-driven approach based on clustering. We establish asymptotic results for our tests and illustrate the methodology in several real data applications.