一种方式分组的随机效应模型中方差分量的可容许估计

吴启光

系统科学与数学 ›› 1983, Vol. 3 ›› Issue (4) : 316-324.

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系统科学与数学 ›› 1983, Vol. 3 ›› Issue (4) : 316-324. DOI: 10.12341/jssms09317
论文

一种方式分组的随机效应模型中方差分量的可容许估计

    吴启光
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ADMISSIBLE ESTIMATES OF VARIANCE COMPONENTS IN A RANDOM-EFFECT MODEL OF ONE-WAY CLASSIFICATION

    Wu Qiguang
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摘要

考虑一种方式分组的随机效应模型 (1.1) 这里, 相互独立, 都是未知的参数。记此处,1_κ为元素都是1的k维向量,当不引起混淆时,省去脚标k。我们可把模型(1.1)改...

Abstract

Consider a random-effect model Y_(ij)=μ+φ_i +ε_(ij), i=1, ..., n, j=1, ..., k, where n≥2, φ_1, …, φ_n,ε_(11), …, ε_(1k), …, ε_(n1), …, ε_(nk) are independent, β~2≥0 are parameters. Let Y=(Y_(11), …, y_(1k),…, y_(n1),…, y_(nk))'. The sufficient conditions for an estimate of pσ~2 + qβ~2 to be admissible in the class {Y'AY: A is any real symmetric matrix} or in the class {Y'AY: A≥0} under the loss function σ~(-4)(d—pσ~2—qβ~2)~2 are given and families of admissible estimators within the class that contains all the estimates for pσ~2 + qβ~2 when φ_i~N(0, β~2) and ε_(ij)~N(0, σ~2), i=1,…, n, j=1, …, k, are derived. Some classes of admissible estimators for (σ~2, β~2) in {(Y'A_1Y, Y'A_2Y): A_1 and A_2 are real symmetric matrices} or in {(Y'A_1Y, Y'A_1Y): A_1≥0, A_2≥0} with the loss function σ~_(-4)[(d_1—σ~2)~2 + (d_2—β~2)~2] are found. Also, it is proved that the usual estimate of (σ~2,β~2) is inadmissible.

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吴启光. 一种方式分组的随机效应模型中方差分量的可容许估计. 系统科学与数学, 1983, 3(4): 316-324. https://doi.org/10.12341/jssms09317
Wu Qiguang. ADMISSIBLE ESTIMATES OF VARIANCE COMPONENTS IN A RANDOM-EFFECT MODEL OF ONE-WAY CLASSIFICATION. Journal of Systems Science and Mathematical Sciences, 1983, 3(4): 316-324 https://doi.org/10.12341/jssms09317
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