Abstract:
Consider the heteroscedastic regression model: y_i=x_{i ^β} +g(ti)+σ_ie_i ,i=1,2,...,n,where Here σ_i=f(u_i), (x_i,t_i,u_i)Here the design points (x_it_i,u_i) are known and nonrandom, g and ^_f are unknown functions , and β is the parameter needed to be estimated,e_i is the random error and a martingale difference sequence in relation to the undecreasing σ-algebra series {F_i,i≥1}. For the least squares estimator βn and the weighted least squares estimator βn of β given in [1] based on the family of nonparametric estimates of g(^.) and f^_(.), the authors establish their strong consistency under suitable conditions, thereby improve the the result where e_i is iid in [6].

Key words: Partial linear model, Least squares estimator, Weighted least squares
estimator, Strong consistency, Martingale difference