侯波.关于线性模型中误差方差估计中心极限定理余项的非一致性估计[J].数学研究及应用,1986,6(4):133~142
关于线性模型中误差方差估计中心极限定理余项的非一致性估计
Noncompatible estimation of the residuai sum of sguares of central limit theorem in linear model
投稿时间:1983-06-27  
DOI:10.3770/j.issn:1000-341X.1986.04.033
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侯波 中国科技大学 
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      in linear models, the error varianceσ2 of random errors is usually estimat-ted by the residual sum of squares (divided by a su ita ble degree of free-dom), based on the first n observation, (denote it by σn2). it is well known t that under certain conditions, the distribution of this estimate, when standardised, converges to the standard normal distribution. In this paper, it is shown that |Gn(x)-Ф(x)|=O(n-δ/2(1+|x|)-(2+δ)). when the errors are indepedent (maynot be identically distributed) and their 4 + 2δ order moments exist, where Gn(x) is the distribution of (σn22/(varσn2)1/2,Ф(x)=1/(2π)1/2-∞xe-r2/2dt.
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