Partially linear models on Riemannian manifolds

TL;DR

This paper develops estimators for partially linear models where the explanatory variables lie on a Riemannian manifold, combining model flexibility with complex geometric structures, and demonstrates their theoretical properties and practical performance.

Contribution

It introduces novel estimators for partially linear models with Riemannian manifold-valued variables, proving their asymptotic normality and validating through simulations and real data.

Findings

Estimator of eta is asymptotically normal.

Simulation studies show good estimator performance.

Application to real data demonstrates practical utility.

Abstract

In partially linear models the dependence of the response y on (x^T,t) is modeled through the relationship y=\x^T \beta+g(t)+\epsilon where \epsilon is independent of (x^T,t). In this paper, estimators of \beta and g are constructed when the explanatory variables t take values on a Riemannian manifold. Our proposal combine the flexibility of these models with the complex structure of a set of explanatory variables. We prove that the resulting estimator of \beta is asymptotically normal under the suitable conditions. Through a simulation study, we explored the performance of the estimators. Finally, we applied the studied model to an example based on real dataset.