L_r Convergence And Complete Convergence For AANA Random Variables And Its Application In Semiparametric Models

Limit theory is an important research direction of probability theory and mathematical statistics,and mainly research the convergence of random vari-able sequence and the sequence of distribution function.In practical problems,a large number of random events is not independent,so the concept of depen-dency followed.It has been widely used in many fields,such as actuarial insurance,survival analysis,economic decision making and so on.This pa-per discusses the complete convergence,complete moment convergence and Lr convergence for a sequence of asymptotically almost negatively associated(for short,A AN A)random variables,and gives a simple application on the semiparametric regression model.Firstly,we study the complete moment convergence and Lr convergence for maximal partial sums of AANA random variables under some general con-ditions and moment inequalities.The results obtained in the paper generalize some corresponding ones for negatively associated(for short,NA)random variables.Secondly,by using the truncation method,we obtain the Lr convergence and the complete convergence for weighted sums of a sequence of AANA ran-dom variables,which is stochastically dominated by a random variable X.As an application of complete convergence,the Marcinkiewicz-Zygmund type strong law of large numbers for AANA random variables is obtained.At last,this paper is concerned with the semiparametric regression model y_i=x_i?+g(ti)+?_ie_i,i=1,2,...,n,n?1,where ?_i~2=f(u_i),(x_i,t_i,u_i)are known fixed design points.When the random errors ei are AANA ran-dom variables,some results on consistency for least squares estimators and weighted least squares estimators of ? and g under some suitable conditions are investigated,especially the p-th(p>1)moment consistency and complete consistency.The results obtained in the paper generalize some corresponding ones for negatively associated random variables.And,we use R software to simulate and verify the validity of the theoretical results.