| Mathematical statistics is the basis of statistical analysis.Due to the needs in practical produce,the statistical model established by mathemat-ical analysis method has gradually become one of the focuses of statistical research.Nonparametric statistics is an important branch of statistics and many nonparametric methods are mainly based on some asymptotic proper-ties of statistics.Therefore,the asymptotic properties of statistics are crucial to handle the problems in statistical models.In this paper,we mainly study the asymptotic theories of estimators in EV regression model,semiparametric regression model and nonlinear regres-sion model,which mainly deal with least square estimator and GM estimator.It should be noted that GM estimator(an estimator involved with integral form)has higher accuracy than PC estimator,when the sample size is not large enough.We discuss the problem about complete f-moment convergence for weighted sums of END random variables,which improves and generalizes the corresponding ones in existing achievements.Then we get the complete consistency for least squares estimators of unknown parameters in EV regres-sion model under END random errors,and then give the numerical simulation.From the model itself,we study the moment consistency for least squares es-timator of unknown parameter and function in the semiparametric regression model with ?-mixing errors under the condition of weaker moment condition;at the same time,we give the numerical simulation.We study the asymptotic results for GM estimator in the nonlinear regression model under ?-mixing er-rors,including the r-th moment consistency and asymptotic normality.After that,a simulation satisfying the theoretical conditions is given according to theorems.The results of this paper enrich and improve the probability limit the-ory for dependent and mixing random variables and asymptotic theory for estimators in the important statistical models,and have practical significance. |
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