Extrapolation Estimation for Nonparametric Regression with Measurement Error

TL;DR

This paper introduces a fast extrapolation algorithm for nonparametric regression with measurement error, avoiding simulation steps and providing exact extrapolation forms, supported by theoretical analysis and empirical validation.

Contribution

It proposes a novel extrapolation algorithm that reduces computational complexity and offers exact extrapolation forms in nonparametric regression with measurement error.

Findings

The method significantly reduces computational time compared to classical approaches.

The proposed estimator has desirable large sample properties.

Simulation studies and real data applications demonstrate its effectiveness.

Abstract

For the nonparametric regression models with covariates contaminated with normal measurement errors, this paper proposes an extrapolation algorithm to estimate the nonparametric regression functions. By applying the conditional expectation directly to the kernel-weighted least squares of the deviations between the local linear approximation and the observed responses, the proposed algorithm successfully bypasses the simulation step needed in the classical simulation extrapolation method, thus significantly reducing the computational time. It is noted that the proposed method also provides an exact form of the extrapolation function, but the extrapolation estimate generally cannot be obtained by simply setting the extrapolation variable to negative one in the fitted extrapolation function if the bandwidth is less than the standard deviation of the measurement error. Large sample properties of the proposed estimation procedure are discussed, as well as simulation studies and a real data example being conducted to illustrate its applications.