Asymptotic properties of wavelet estimators in a semi-parametric EV models with ANA errors

Abstract In this paper, when the errors in the semi-parametric errors-in-variables model are asymptotic negatively associated (or ρ − , for short) random variables, the estimators of parameter, non-parameter, and error variances in the model are $\widehat{\beta}_{n}$ , $\widehat{g}_{n}(t)$ , and $ \widehat{\sigma}_{n}^{2}$ , respectively, by using wavelet smoothing and least square method. Under some general assumptions, we also establish some results on the strong consistency of the estimators. Furthermore, simulations are conducted to assess the finite sample behavior of the estimators and confirm the validity of the theoretical results.