A new class of generalized Bayes minimax ridge regression estimators
A new class of generalized Bayes minimax ridge regression estimators
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DOI：
10.1214/009053605000000327
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发表时间：
2005-08-01
影响因子：
4.5
通讯作者：
Strawderman, WE
中科院分区：
文献类型：
--
作者：
Maruyama, Y;Strawderman, WE
设y=Aβ+epsilon，其中y是观测值的N×1向量，β是未知回归系数的p x i向量，A是N x p设计矩阵，E是具有未知尺度参数a的球对称误差项.我们考虑一般二次损失函数下的估计，特别地，推广了Strawderman[J.Amer统计量]的工作.阿索克。73(1978)623-627]和Casella[Ann.统计学家。8(1980)1036-1056，J.Amer。统计学家。阿索克。80(1985)753-758]通过寻找贝塔的自适应极小极大估计(在正态假设下，它也是广义贝叶斯)，它比通常的最小二乘估计具有更大的数值稳定性(即，更小的条件数)。特别是，我们给出了这类估计量的一个子类，令人惊讶的是，它具有非常简单的形式。我们还证明了在一定条件下，正态情形下的广义Bayes极小极大估计在球对称误差的一般情形下也是广义Bayes估计和极小极大估计。
Let y = A beta + epsilon, where y is an N x 1 vector of observations, beta is a p x I vector of unknown regression coefficients, A is an N x p design matrix and E is a spherically symmetric error term with unknown scale parameter a. We consider estimation of under general quadratic loss functions, and, in particular, extend the work of Strawderman [J. Amer Statist. Assoc. 73 (1978) 623-627] and Casella [Ann. Statist. 8 (1980) 1036-1056, J. Amer. Statist. Assoc. 80 (1985) 753-758] by finding adaptive minimax estimators (which are, under the nonnality assumption, also generalized Bayes) of beta, which have greater numerical stability (i.e., smaller condition number) than the usual least squares estimator. In particular, we give a subclass of such estimators which, surprisingly, has a very simple form. We also show that under certain conditions the generalized Bayes minimax estimators in the normal case are also generalized Bayes and minimax in the general case of spherically symmetric errors.