Robust and adaptive functional logistic regression

Abstract

A novel family of robust estimators for the functional logistic regression model is introduced and studied. The estimators are based on the concept of density power divergence between densities and may be formed with any combination of lower rank approximations and penalties, as the need arises. Uniform convergence and high rates of convergence with respect to the commonly used prediction error are established under general assumptions. Importantly, these assumptions permit random tuning parameters thereby allowing for the robustness of the estimators to adapt to the data. This leads to estimators with high efficiency in clean data and a high degree of resistance towards atypical observations. The highly competitive practical performance of the proposed family of estimators is illustrated on a simulation study and a real data example involving gait analysis and which includes atypical observations.