Asymptotic Distribution Of M Estimator For Dependent Random Sample

Theoretical research and practical experience shows that,the traditional estimation methods of parameters,such as moment estimation,least squares method,although the asymptotic efficiency is very high,but if the analysis data in some deviate from the overall composition,these methods are not ideal,therefore,the traditional parameter estimation method is lack of robustness.In recent decades,statisticians proposed many alternative methods,the M method is one of the most important and most important research results.The assumption that the random variables are independent is not very suitable in many cases,and many variables are dependent on the actual life,so people often study dependent random variables.Negative association(short in NA),negatively superadditive dependence(short in NSD),asymptotically almost negatively dependent(short in AANA)and widely orthant dependent(short in WOD)random sequence are common dependence.Many scholars have studied the M estimator of independent random variables,literature [12,44] systematically studied the properties of independent random variables.On the basis of the predecessors,this paper further discusses the dependent random samples and studies the asymptotic distribution of M estimator,the main contents are as follows:In chapter 2,under very general conditions,by using some lemmas and the truncation methods,the asymptotic normality of the M estimator for the random samples of NA,NSD,AANA and WOD are obtained.In chapter 3,considering long memory in volatility models,under the appropriate conditions,the asymptotic normality of M estimator and nonuniform Berry-Esseen bounds are proved by the martingale difference.Then,the theoretical application of the model is given,and the validity of the model is illustrated by a practical example.The conclusions not only generalizes the corresponding conclusions of independent random variables,but also obtained the convergence rule of limit distribution of partial sums for long memory in volatility models,and generalizes the asymptotic theory of M estimator in linear models.