Robust Estimators in Partly Linear Regression Models on Riemannian Manifolds

TL;DR

This paper develops robust estimation methods for partially linear regression models where predictors lie on Riemannian manifolds, ensuring consistency and asymptotic normality, with practical validation through simulations and real data.

Contribution

It introduces a new family of robust estimators for regression parameters and functions on Riemannian manifolds, including a robust cross-validation method for smoothing parameter selection.

Findings

Estimators are consistent and asymptotically normal.

Robust cross-validation effectively selects smoothing parameters.

Proposed methods perform well with small samples and contaminated data.

Abstract

Under a partially linear models we study a family of robust estimates for the regression parameter and the regression function when some of the predictor variables take values on a Riemannian manifold. We obtain the consistency and the asymptotic normality of the proposed estimators. Also, we consider a robust cross validation procedure to select the smoothing parameter. Simulations and application to real data show the performance of our proposal under small samples and contamination.