苏淳.线性模型中误差方差估计的指数收敛速度[J].数学研究及应用,1983,3(2):81~84 |
线性模型中误差方差估计的指数收敛速度 |
Exponential Convergence Rates of Error-variance Estimates in Linear Models |
投稿时间:1981-06-29 |
DOI:10.3770/j.issn:1000-341X.1983.02.014 |
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英文摘要: |
Suppose given a linear model yj=x'jβ+μj, j=1,2,…, The random errors all have a mean zero and unknown variance σ2, 0<σ2<∞. Let σn2 be the estimate of σ2 based on the residual sum of squares and calculated from (xj, yj), j=1,…,n. In this paper we show that if μ1,μ2,…, are independent but not necessarily identically distributed, and some further conditions on {μj} and (x1|…|xn) are satisfied, then for any ε>0 there exist constant ρε, 0<ρε<1, Such that P(|σn2-σ2|≥ε)=O(ρεn). |
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