Testing the Missing Completely at Random Assumption for Functional Data

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 are 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 systematic approach based on clustering.

We establish asymptotic results for our tests and illustrate the methodology in several real data applications.