Asymptotic Properties Of M-estimators In Linear Models For NSD Errors

It is well known that linear regression models have received much attentions for their enormous applications in various areas such as engineering technology,economics and social sciences.Unfortunately,there exists a problem that the classical LS estimator for these models is sensitive to outliers and lack robustness.To overcome this defect,Huber proposed the M-estimate(see Huber[1])in 1964.Whereas,most of the asymptotic properties for M-estimate rely on the independence errors.As Huber[1] claimed that the independence assumption on the errors was a serious restriction.Its practically essential and imperative to explore the case of dependent errors,which is a theoretically challenging.Comparing with negatively associative(NA),negatively superadditive dependent(NSD)contains more widely sequences,and it has received an increasing attention for its enormous research value in copula theory and economics.In this paper,we study the asymptotic properties of M-estimators in linear models for NSD errors.In chapter 2,using the trunkated method,we obtain a central limit theorem and a weighted sums of central limit theorem for NSD random variables.In chapter 3,we investigate the asymptotic normality of M-estimators in linear models(contain constant and without constant term)with NSD errors.In chapter 4,we concern with the M-test problem of the regression parameters with NSD random errors.Also,we obtain the asymptotic distribution of test statistic base on M-criterion and establish the consistent estimates of the redundancy parameters which involved in the asymptotic distribution.In chapter 5,some Monte Carlo simulations are given to illustrate the presented theoretical results via evaluating the parameter estimates and calculating the powers.The conclusions not only promote the corresponding conclusion in Rao [11] and Bai [12] when the error is independent,but also extend the asymptotic theory in Zhao [8].