Robust and efficient estimation of nonparametric generalized linear models

TL;DR

This paper introduces a new family of nonparametric spline estimators for generalized linear models that are robust to outliers, easy to implement, and can be tuned for high efficiency, with proven fast convergence and strong empirical performance.

Contribution

It proposes a novel class of penalized power divergence spline estimators that improve robustness and efficiency in generalized linear models.

Findings

Estimators converge at a fast rate under weak assumptions.

High protection against outliers demonstrated.

Competitive performance shown in simulations and real data.

Abstract

Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these shortcomings we introduce and study a family of nonparametric full rank and lower rank spline estimators that result from the minimization of a penalized power divergence. The proposed class of estimators is easily implementable, offers high protection against outlying observations and can be tuned for arbitrarily high efficiency in the case of clean data. We show that under weak assumptions these estimators converge at a fast rate and illustrate their highly competitive performance on a simulation study and two real-data examples.