Symmetrical Convergence Rates and Asymptotic Properties of Estimators in a Semi-Parametric Errors-in-Variables Model with Strong Mixing Errors and Missing Responses

This paper considers a semi-parametric errors-in-variables (EV) model, ηi=xiβ+g(τi)+ϵi, ξi=xi+δi, 1⩽i⩽n. The properties of estimators are investigated under conditions of missing data and strong mixing errors. Three approaches are used to handle missing data: direct deletion, imputation, and the regression surrogate. Furthermore, estimators for the coefficient β and the nonparametric function g(·) are obtained. Notably, both estimators achieve strong consistency at a rate of o(n−1/4), exhibiting a symmetry in their convergence rates, and they also demonstrate asymptotic normality. Additionally, the validity of our theoretical results is supported by simulations demonstrating the finite sample behaviour of these estimators.