具有p个方差分量的线性模型的Beyes二次估计及可容许估计的非负性
BAYES QUADRATIC ESTIMATES AND NONNEGATIVENESSOF ADMISSIBLE ESTIMATES IN LINEAR MODELSWITH p VARIANCE COMPONENTS
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摘要: 本文对具有 p 个方差分量的线性模型讨论了方差分量线性函数的 Bayes 不变二次估计问题,给出了 Bayes 不变二次估计(无偏和有偏)的显示表达式,并且证明了它们在各自考虑的类中形成了可容许估计的完全类.在可容许估计的完全类中,还讨论了非负参数函数的非负估计问题,给出了可容许的非负定估计存在的充要条件。Abstract: In this paper,linear models with p variance components are considered and the explicit expressions for Bayes invariant quadratic estimates,biased and unbiased,are presented and proved these estimates to cover the entire class of admissible ones in the considered classes.The necessary and sufficient conditions for the existence of admissible nonnegative definite quadratic estimates,biased and unbiased,are given.
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