单向分类随机模型方差分量的经验Bayes估计

对于在质量控制、生物育种以及计量经济等方面有着广泛应用的单向分类随机模型 其中y_(ij)为观测数据,ε_i～N(0,σ_1~2)为随机效应,ε_i～N(0,σ_2~2)是随机误差,通常要求考虑对其参数μ,σ_1~2,σ_2~2作出估计,特别是对方差分量σ_1~2,σ_2~2的估计。而在目前常见的估计方法中,大都有一个共同的缺点,即不能保证方差分量估计的非负性。本文采用经验Bayes方法,在平方损失下,利用密度函数及其偏导数的核估计构造出方差分量的一个经验Bayes估计,这个估计是非负的。并证明了这种估计是渐近最优的,在一定条件下,其收敛速度可任意地接近于0(n~(-1/2)。

An Empirical Bayes Estimator of Variance Components in One-Way Random Model

Model with components of variance is frequently used in quality control, animal breeding experiments, and elsewhere. For this model, various estimators of variance components have been proposed.But they have a common shortcoming: the estimators are not guaranteed to be nonnegative. In this paper we studied the empirical Bayes estimation of variance components in the one-way random model with balanced data. For the square loss function, an empirical Bayes estimator of the model parameters is constructed by the estimation of kernel density and its partial derivatives. The estimator is nonnegative. It is shownthat the estimator is asymptotically optimal with its convergence rate arbitrarilyclose to 0(n-1/2) under suitable conditions.