Supervised classification for a family of Gaussian functional models

TL;DR

This paper derives explicit optimal classification rules for Gaussian functional data with triangular covariance functions, enabling consistent nearest neighbors and effective plug-in classifiers validated through simulations and real data.

Contribution

It provides explicit formulas for optimal classifiers in Gaussian functional data and demonstrates their practical use for consistent and plug-in classifiers.

Findings

Explicit optimal classification rules derived for Gaussian processes.

Nearest neighbors classifier shown to be consistent for the specified class.

Plug-in classifiers perform well in simulations and real data.

Abstract

In the framework of supervised classification (discrimination) for functional data, it is shown that the optimal classification rule can be explicitly obtained for a class of Gaussian processes with "triangular" covariance functions. This explicit knowledge has two practical consequences. First, the consistency of the well-known nearest neighbors classifier (which is not guaranteed in the problems with functional data) is established for the indicated class of processes. Second, and more important, parametric and nonparametric plug-in classifiers can be obtained by estimating the unknown elements in the optimal rule. The performance of these new plug-in classifiers is checked, with positive results, through a simulation study and a real data example.