Consistency of estimators for semiparametric regression model under mixing errors

The aim of this paper is to investigate the semiparametric regression model with φ mixing and ψ mixing errors.The methods of least squares and weight function are used to define the estimators βm,n andgm,n(x) for unknown parameter β and unknown function g,respectively.The strong consistency and the moment consistency for these estimators are proved under some weaker conditions by using the moment inequalities of mixing sequences and the property of the convex function,which generalize the cited results.