Nonparametric Identification and Estimation with Non-Classical Errors-in-Variables

TL;DR

This paper develops methods for nonparametric identification and estimation of regression functions when covariates are measured with non-classical errors, using instrumental variables and small error approximations.

Contribution

It introduces a new framework for nonparametric identification with non-classical measurement errors and proposes estimators with known convergence rates.

Findings

Identification achieved under weak conditions

Proposed estimators have established convergence rates

Applicable to models with non-classical measurement errors

Abstract

This paper considers nonparametric identification and estimation of the regression function when a covariate is mismeasured. The measurement error need not be classical. Employing the small measurement error approximation, we establish nonparametric identification under weak and easy-to-interpret conditions on the instrumental variable. The paper also provides nonparametric estimators of the regression function and derives their rates of convergence.