Xi, Mengmei; Wang, Rui; Yu, Wei; Shen, Yan; Wang, Xuejun Asymptotic properties for the estimators in heteroscedastic semiparametric EV models with \(\alpha\)-mixing errors. (English) Zbl 1465.62133 Statistics 54, No. 6, 1232-1254 (2020). Summary: In this paper, the heteroscedastic semiparametric errors-in-variables (EV) model, \(y_i = \xi_i \beta + g(t_i) + \epsilon_i\), \(x_i = \xi_i + \mu_i\), \(1 \le i \le n\), is considered, where \(\epsilon_i = \sigma_i e_i\), \(\sigma^2_i = f(u_i)\), \(\beta\) is an unknown parameter to be estimated and \(g(\cdot)\) and \(f(\cdot)\) are unknown functions to be estimated. Under some suitable conditions, asymptotic properties for the estimators of \(\beta\), \(g(\cdot)\) and \(f(\cdot)\) are presented based on \(\alpha\)-mixing random errors. In addition, finite sample behavior of the estimators is provided via simulations to verify the validity of the theoretical results. MSC: 62J12 Generalized linear models (logistic models) 62G20 Asymptotic properties of nonparametric inference Keywords:semiparametric errors-in-variables (EV) model; EV regression model; \(\alpha\)-mixing errors; least squares estimator; strong consistency PDFBibTeX XMLCite \textit{M. 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