Asymptotic Properties Of M Estimator In Linear Regression Model With Asymptotically Almost Negatively Associated Errors

Research and practice have shown that, a typical way in linear regression models—least squares estimate,might be very bad in some conditions.For recent half century,statistics have found many methods to resolve it, of which M method has attracted the greatest attention and produced massive effective results.M estimator is a very important estimate method, it contains the classical estimate methods of least squares estimate and least absolute deviation estimate.The assumption that the random variables are independent is not very suitable in many cases, so people often study the case of dependent random variables, the asymptotically almost negatively associated sequence(short in AANA) is an important one.many scholars have studied M estimator of linear regression model: for independent errors, literature [9-11] systematically studied the large sample properties of M estimator, some deeply conclusions were obtained; for NA errors,under the appropriate condition, literature [12,13] got the strong consistency of dependent errors situations could be seen in literature [14,15], etc. However, we have not seen the situation of AANA errors.For this reason, the paper considers the linear regression model with AANA errors, and studies the asymptotic properties of M-estimator.There are four chapters in this thesis.In chapter 1,we simply introduce some important literature on M estimator in the linear regression model.In chapter 2 we discuss the weak consistency of M-estimator of parameter in linear regression model with asymptotically almost negatively associated errors,and extend the corresponding conclusions of linear regression model for the situation of independent errors, negatively associated errors and so on.In chapter 3,the strong consistency of M estimator of parameter is investigated, and Bernstein type inequality for AANA random variables are also obtained, which extend the corresponding results for negatively associated random variables.In chapter 4,the asymptotic normality of M estimator of parameter is studied, and central limit theorem for AANA random variables are also obtained, and extend the corresponding conclusions of linear regression model for the situation of independent errors, negatively associated errors and so on.