摘要
设有线性模型Y_(ij)=β_0+σ_0e_(ij),i=1,2,…,n,…,j=1,2,…,N_i。此处{e_(ij)}为独立同分布,且其均值为零,方差为1。本文提出对β_0的随机加权估计,形如(8)所示的β_n,在e_(11)～N(0,1)和N_i≥6的条件下,我们于文中给出了β_n是β_0相合估计的充要条件,并进一步给出了β_0的大样本置信区间。此外,在非正态情形,我们提出了β_n是β_0相合估计的另一个定理。
Consider the linear model Fij = β0 + σieij, i = 1, 2,…, n,…,j = 1, 2, …, Ni, Where {eij} are Variance 1. Introduce a rondomly weighted estimate βn difined by (8). Assuming e11- N(0, 1) and Ni ≥6, this paper gives a necessary and sufficient condition for βn to be a consistent estimate of β0, and under some further restrictions a normal approximation for βn is estabilished which can be used in constrcting a large sampl confidence interval of β0. Finally, in the non-normal case a theorem about the consistency of βn is proved.
