| Limit theory is one of the important research directions of probability theory and mathematical statistics.But most random events often are not independent by practical considerations.So the concept of dependency emerged as the times require.It has good prospects for application,and it has a wide range of development space in our daily life,such as risk assessment,multivariate statistical analysis,statistical decision method,financial analysis,weather forecast,engineering calculation,etc.In this paper,we will investigate the complete convergence and complete mo-ment convergence of the weighted sums of ANA?Asymptotically Negatively Associ-ated?random variables.Complete convergence and complete moment convergence of the weighted sums of ANA random variables are studied by using the moment of inequalities and the condition of random control for ANA random variables.Then we obtained the Marcinkiewicz-Zygmund type strong law of large numbers for weight-ed sums of ANA random variable.The results significantly improve and extend the corresponding ones of Chen and Sung[25].Based on conclusions above,we further investigate the consistency for the weighted estimator of nonparametric regression model under the ANA random errors and present the numerical simulations of the results.Furthermore,with the help of some probability inequalities and some con-ditions,we first establish a general result on the complete convergence for weighted sums of linear process based on ANA random errors.Based on the result above,we further study the consistency for the weighted estimator of semi-parametric regres-sion model under the assumption of ANA random errors and present some numerical simulations to verify our result.The results obtained significantly improve the con-clusions of related results in the existing literature.Therefore,the results obtained in this paper further enrich and generalize the and large sample theory of statistics for ANA random variables and probability limit theory. |
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