Semi-functional partial linear regression with measurement error: An approach based on $k$NN estimation

TL;DR

This paper introduces a semi-functional partial linear regression model that handles measurement error in the parametric component using $k$-NN estimators, with theoretical and empirical validation.

Contribution

It proposes a novel $k$-NN based estimation approach for semi-functional regression with measurement error, including asymptotic analysis and practical demonstrations.

Findings

Estimators perform well in finite samples

Asymptotic properties are established

Application demonstrates practical usefulness

Abstract

This paper focuses on a semiparametric regression model in which the response variable is explained by the sum of two components. One of them is parametric (linear), the corresponding explanatory variable is measured with additive error and its dimension is finite ($p$). The other component models, in a nonparametric way, the effect of a functional variable (infinite dimension) on the response. $k$-NN based estimators are proposed for each component, and some asymptotic results are obtained. A simulation study illustrates the behaviour of such estimators for finite sample sizes, while an application to real data shows the usefulness of our proposal.