线性模型中误差方差估计推广的Berry-Esseen界限

在线性模型中随机误差的方差常用剩余平方和除以适当的自由度来估计,陈希孺教授(1981),白志东、赵林城(1982)在随机误差具有6阶矩的假设条件下,证明了这一估计经标准化后其分布以理想的速度O(1/n~(1/2))收剑于标准正态分布。在本文中,我们把这一结果推广到更一般的情形中,即在误差具有4+2δ(0<δ≤1)阶矩的假设条件下,证明了理想的收敛速度O(n~(-δ)/~2)。这一结果与独立变量和的情形相同。

THE EXTENDED BERRY-ESSEEN BOUNDS FOR ERROR VARIANCE ESTIMATES N LINEAR MODELS

In linear models, the error variance of random errors is usually estimated by the residual sum of squares (divided by a suitable degree of freedom). Under some restrictions imposed on the 6th moments of random errors, Prof. Chen Xiru(1981), Bai and Zhao (1982) Proved that the distribution of this estimate, when standardized, converges to the standard normal distribution with the ideal rate of o(1/√n). In this paper, we extended this result to the more general case, obtaind the ideal convergence rate O(n~(-δ)/~2), under some restrictions imposed on the (4+2δ)-th moments of error sequence, where O<δ<1. This makes our result comparable with the one in the case of sums of independent variables.