Strong consistency of estimators for heteroscedastic partly linear regression model under dependent samples

In this paper we are concerned with the heteroscedastic regression model y_i = x_iβ + g(t_i) + σ _ie_i 1 ≤ i ≤ n) under correlated errors e _i, where it is assumed that σ_i² = f(u_i), the design points (x_i, t_i, u _i) are known and nonrandom, and g and f are unknown functions. The interest lies in the slope parameter β. Assuming the unobserved disturbance e_i are negatively associated, we study the issue of strong consistency for two different slope estimators: the least squares estimator and the weighted least squares estimator. ©2002 by North Atlantic Science Publishing Company