Extrapolation estimation in parametric regression models with measurement error

Abstract

For the general parametric regression models with covariates contaminated with normal measurement errors, an alternative method to the traditional simulation extrapolation algorithm is proposed 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 providing a possibility of reducing the computational time or the Monte Carlo simulation error. 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.