【摘 要】
：
Descriptive analysis of sample survey data estimates means, totals and their variances in a design framework (see for example Haslett, 1985). When analysis
【机 构】
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MasseyUniversity,NewZealand
【出 处】
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The 24th International Workshop on Matrices and Statistics(第
论文部分内容阅读
Descriptive analysis of sample survey data estimates means, totals and their variances in a design framework (see for example Haslett, 1985). When analysis is extended to linear models, the standard design-based method for regression parameters includes inverse selection probabilities as weights, ignoring the joint selection probabilities. When these joint selection probabilities are included to improve estimation, and the error covariance is not a diagonal matrix, a proof will be given that the unbiased sample based estimator of the covariance is the Hadamard product of the population covariance, the elementwise inverse of selection probabilities and joint selection probabilities, and a sample selection matrix of rank equal to the sample size. This Hadamard product is however not always positive definite, which has implications for best linear unbiased estimation. Rao (1968) provides conditions under which a change in covariance structure leaves BLUEs unchanged. The results have been extended by Haslett and Puntanen (2010) to BLUPs, and to BLUEs and BLUPs. Interestingly, this class of "equivalent" matrices for linear models includes matrices that are not positive semi-definite.
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