Statistical classification for partially observed functional data via filtering

TL;DR

This paper develops a kernel-based classifier for functional data with missing segments, applicable to both training and new observations, without assuming missing completely at random, and proves its strong consistency.

Contribution

It introduces a novel kernel classifier for partially observed functional data that does not require missing at random assumptions and proves its strong consistency.

Findings

Classifier performs well in numerical experiments

No assumptions on missing data mechanism required

Strong theoretical consistency established

Abstract

This article deals with the problem of functional classification for L2-valued random covariates when some of the covariates may have missing or unobservable fragments. Here, it is allowed for both the training sample as well as the new unclassified observation to have missing fragments in their functional covariates. Furthermore, unlike most previous results in the literature, where covariate fragments are typically assumed to be missing completely at random, we do not impose any such assumptions here. Given the observed segments of the curves, we construct a kernel-type classifier which is quite straightforward to implement in practice. We also establish the strong consistency of the proposed classifier and provide some numerical examples to assess its performance in practice.