Robust estimation for functional logistic regression models

TL;DR

This paper introduces a robust estimation method for functional logistic regression models that enhances reliability and stability, especially in the presence of atypical or contaminated functional covariates, supported by theoretical and empirical validation.

Contribution

It adapts finite-dimensional robust practices to functional data, providing consistent estimators with proven convergence rates and demonstrating improved stability over traditional methods.

Findings

Estimators are consistent under regularity conditions.

The method shows robustness against contaminated data.

Numerical studies confirm finite sample stability.

Abstract

This paper addresses the problem of providing robust estimators under a functional logistic regression model. Logistic regression is a popular tool in classification problems with two populations. As in functional linear regression, regularization tools are needed to compute estimators for the functional slope. The traditional methods are based on dimension reduction or penalization combined with maximum likelihood or quasi--likelihood techniques and for that reason, they may be affected by misclassified points especially if they are associated to functional covariates with atypical behaviour. The proposal given in this paper adapts some of the best practices used when the covariates are finite--dimensional to provide reliable estimations. Under regularity conditions, consistency of the resulting estimators and rates of convergence for the predictions are derived. A numerical study illustrates the finite sample performance of the proposed method and reveals its stability under different contamination scenarios. A real data example is also presented.