Extrapolation Estimation for Parametric Regression with Normal Measurement Error

TL;DR

This paper introduces an accelerated simulation extrapolation algorithm for parametric regression with normal measurement errors, reducing computational time while maintaining statistical properties.

Contribution

It proposes a novel, faster estimation method that directly applies conditional expectation, eliminating the simulation step in measurement error models.

Findings

The estimator is consistent and asymptotically normal.

The method significantly reduces computational time.

Applications include simulations and real data analysis.

Abstract

For the general parametric regression models with covariates contaminated with normal measurement errors, this paper proposes an accelerated version of the classical simulation extrapolation algorithm to estimate the unknown parameters in the regression function. By applying the conditional expectation directly to the target function, the proposed algorithm successfully removes the simulation step, by generating an estimation equation either for immediate use or for extrapolating, thus significantly reducing the computational time. Large sample properties of the resulting estimator, including the consistency and the asymptotic normality, are thoroughly discussed. Potential wide applications of the proposed estimation procedure are illustrated by examples, simulation studies, as well as a real data analysis.