Bayes估计的进一步研究及其Pitman最优性

对线性模型参数,讨论了Bayes估计的Pitman最优性,将已有结果进行了改进,去掉了附加条件,证明了在Pitman准则下,Bayes估计一致优于最小二乘估计(LSE),在此基础上,提出了一种基于先验信息的方差分量估计,通过和基于LSE的方差分量估计作比较,证明了新估计是无偏估计且有更小的均方误差．最后,证明了在Pitman准则下生长曲线模型参数的Bayes估计优于最佳线性无偏估计．

The Farither Study and Pitman Superiority of Bayes Estimate

For the parameters of linear model, the Pitman superiority of Bayes estimate is discussed. The existing conclusion has been improved without the additive conditions. We prove that the Bayes estimate is uniformly superior to the least squares estimate (LSE) under the Pitman closeness criterion. A new variance component estimator proposed based on prior information, compared to the estimator based on LSE, is also unbiased and with smaller mean squares error. Finally, the conclusion that the Bayes estimate of growth curve model performs better than BLUE under the pitman closeness criterion is proved.