Strong consistency of estimators for heteroscedastic partly linear regression model under dependent samples (Q1872622)

Summary: We are concerned with the heteroscedastic regression model \(y_i=x_i \beta+ g(t_i)+ \sigma_ie_i\), \(1\leq i\leq n,\) under correlated errors \(e_i\), where it is assumed that \(\sigma^2_i= f(u_i)\), 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 \(\beta\). Assuming the unobserved disturbances \(e_i\) 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.