NSD序列加权和的完全收敛性及其应用

Complete Convergence for the Weighted Sums of NSD Sequences and Its Application

研究了NSD(negatively superadditive dependent)随机变量序列的极限定理.利用截尾技术和NSD随机变量序列的性质讨论了NSD随机变量加权和Sn=n∑i=1 anixi的完全收敛性,并将其结果应用于含参数β的最小二乘估计的线性回归模型中及关于g的权函数非参数回归模型估计中,分别得到了强相合性.

In this paper,we investigate some limit theorems for weighted sums of sequences of NSD random variables.By using the truncation technique and the properties of sequences of NSD random variables,we obtain the complete convergence for weighted sums of sequences of NSD random variables.Applying these results to the linear regression model containing the least square estimation of parameterβ,and to the estimation of the nonparametric regression model of the weight function about g,we obtain their strong consistency.