Nonparametric regression with nonparametrically generated covariates

TL;DR

This paper develops a theoretical framework to understand how using estimated covariates affects the statistical properties of nonparametric regression estimators, applicable in various complex modeling scenarios.

Contribution

It provides the first general theory quantifying the impact of generated covariates on nonparametric regression estimators' asymptotic behavior.

Findings

Derived a stochastic expansion for estimators with generated covariates

Established rates of consistency accounting for covariate estimation

Characterized asymptotic distributions considering generated covariates

Abstract

We analyze the statistical properties of nonparametric regression estimators using covariates which are not directly observable, but have be estimated from data in a preliminary step. These so-called generated covariates appear in numerous applications, including two-stage nonparametric regression, estimation of simultaneous equation models or censored regression models. Yet so far there seems to be no general theory for their impact on the final estimator's statistical properties. Our paper provides such results. We derive a stochastic expansion that characterizes the influence of the generation step on the final estimator, and use it to derive rates of consistency and asymptotic distributions accounting for the presence of generated covariates.