Abstract:

In this paper, the heteroscedastic semiparametric errors-in-variables (EV) model, y_i = ξ_iβ + g(t_i) + ε_i, x_i = ξ_i + μ_i, is considered, where ε_i = σ_ie_i, σ²_i = f(u_i), β is an unknown parameter to be estimated, and g(·) and f(·) are unknown functions to be estimated. Under the assumption of α-mixing random errors, we establish the asymptotic normality for estimators of β, g(·) and f(·) in both homoscedastic and heteroscedastic cases. Numerical simulations are conducted to examine the finite-sample performance of the proposed estimators.

2010 AMS Mathematics Subject Classification: Primary 62E20; Secondary 62F12, 62G20.

Keywords and phrases: semiparametric EV regression model, α-mixing errors, least squares estimator, asymptotic normality.