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Allocation in Stratified Sampling as a Game

将分层抽样中的样本分配视为博弈

We consider here the problem of allocating sampling effort among strata when there is no useful information on the within-stratum variability. We show that in a natural game theoretic analogue proportional allocation is a unique good strategy.

AI 解读阅读原文 ↗BibTeX ↓

Allocation in Stratified Sampling as a Game

作为博弈的分层抽样分配

We consider here the problem of allocating sampling effort among strata when there is no useful information on the within-stratum variability. We show that in a natural game theoretic analogue proportional allocation is a unique good strategy.

AI 解读阅读原文 ↗BibTeX ↓

On the Bias of Some Least-Squares Estimators of Variance in a General Linear Model

一般线性模型中若干最小二乘方差估计量的偏差

Watson (1955) investigated the performance of a regression analysis based on the assumption that the error covariance matrix is σ2γ when it is, in fact, σ2γ. In the present paper Watson's results regarding the effects of this type of specification error on the bias of estimators of variance are generalized. In particular, we give, for arbitrary design matrices of full rank, attainable bounds for the bias of the least-squares estimator of the variance of arbitrary linear…

AI 解读阅读原文 ↗BibTeX ↓

On the bias of some least-squares estimators of variance in a general linear model

一般线性模型中若干最小二乘方差估计量的偏差

Watson (1955) investigated the performance of a regression analysis based on the assumption that the error covariance matrix is σ2γ when it is, in fact, σ2γ. In the present paper Watson's results regarding the effects of this type of specification error on the bias of estimators of variance are generalized. In particular, we give, for arbitrary design matrices of full rank, attainable bounds for the bias of the least-squares estimator of the variance of arbitrary linear…

AI 解读阅读原文 ↗BibTeX ↓