Abstract
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.
Published Version
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