Improved Nonnegative Estimation of Variance Components in Balanced Multivariate Mixed Models
Improved Nonnegative Estimation of Variance Components in Balanced Multivariate Mixed Models
复制标题
平衡多元混合模型中方差分量的改进非负估计
DOI：
10.1006/jmva.1994.1051
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发表时间：
1994
影响因子：
1.6
通讯作者：
B. Sinha
中科院分区：
文献类型：
--
作者：
T. Mathew;A. Niyogi;B. Sinha
考虑独立Wishart矩阵S1 W（？）+ ??, q1）和S2 W（？，Q2）在哪里？是未知的正定（p.d.）矩阵，？是未知的非负定（n.n.d.）矩阵和？是已知的正标量。为了估计？，一类估计的形式？？（c，？）=（c/？）{S1/q1？? (S2/q2）}（c？0，？? 1），一致优于无偏估计？？U =（1/？）{S1/q1？S2/q2}，推导出（平方误差损失函数）。得到了n.n.d.形式的估计器？？（c，？）一致优于？联合事实证明，这样一个n.n.d.估计量仅在限制条件下存在。然而，对于一个合适的选择c > 0，？> 0，通过取？？（c，？）结果是神经衰弱。估计，说？？（c，？）+，这是均匀优于？？联合数值结果表明，在均方误差方面，？？（c，？）+ 比这两个都好？U和限制最大似然估计？REML的？类似的结果也得到了非负估计TR？和一个？？a，其中a是任意非零向量。为了估计？我们已经推导出估计量，声称是一致优于无偏估计？？在平方误差损失函数和熵损失函数下，U = S2/q2。我们只能在双变量的情况下才能证明这一点。数值结果报告显示我们提出的估计？的风险改善。
Consider the independent Wishart matrices S1W(? + ??,q1) and S2W(?, q2) where ? is an unknown positive definite (p.d.) matrix, ? is an unknown nonnegative definite (n.n.d.) matrix, and ? is a known positive scalar. For the estimation of ?, a class of estimators of the form ??(c,?) = (c/?){S1/q1 ? ?(S2/q2)} (c ? 0, ? ? 1), uniformly better than the unbiased estimator ??U = (1/?){S1/q1 ? S2/q2}, is derived (for the squared error loss function). Necessary and sufficient conditions are obtained For the existence of an n.n.d. estimator of the form ??(c,?) uniformly better than ?U. It turns out that such an n.n.d. estimator exists only under restrictive conditions. However, for a suitable choice of c > 0, ? > 0, the estimator obtained by taking the positive part of ??(c, ?) results in an n.n.d. estimator, say ??(c, ?) +, that is uniformly better than ??U. Numerical results indicate that in terms of mean squared error, ??(c, ?) + performs much better than both ??U and the restricted maximum likelihood estimator ??REML of ?. Similar results are also obtained for the nonnegative estimation of tr ? and a??a, where a is an arbitrary nonzero vector. For estimating ?, we have derived estimators that are claimed to be uniformly better than the unbiased estimator ??U = S2/q2 under the squared error loss function and the entropy loss function. We have been able to establish the claim only in the bivariate case. Numerical results are reported showing the risk improvement of our proposed estimators of ?.