The Consistency Of Estimators In Nonparametric And Semi-parametric Models Under ?~*-mixing Errors

It is well known that the study of the limit properties of estimators is al-ways the topic of mathematical statistics.While the consistency of estimators is an indispensable problem in the investigations.Consequently,the study of the consistency of estimators in nonparametric and semi-parametric regression models is theoretical meaningful and valuable in application.In this paper,we will investigate the consistency of estimators in nonpara-metric and semi-parametric regression models under ?~*-mixing errors.To ob-tain the consistency of estimators in nonparametric regression model,we first discuss the convergence properties for weighted sums of arrays of ?~*-mixing random variables.By establishing some general moment inequality and tech-nic methods,we obtain the complete moment convergence for weighted sums of arrays of ?~*-mixing random variables and then obtain the complete convergence and Marcinkiewicz-Zygmund type strong law of large numbers for p~*-mixing random variables.These results improve and extend the corresponding ones of Sung[50].Based on the results above,by using some probability inequal-ities we further obtain the complete consistency for the weighted estimator of nonparametric regression model under the ?~*-mixing random errors and present the numerical simulations of the results.Moreover,we also study the strong consistency and moment consistency for the least square estimator of the parametric and the estimator of the unknown function in semi-parametric regression model under the assumption of ?~*-mixing random errors and present some numerical simulations.The results markedly improve the corresponding ones in the literature.Consequently,the results obtained in this paper further enrich and improve the probability limit theory and the large sample theory of statistics for ?~*-mixing random variables.