On improved estimation of normal precision matrix and discriminant coefficients
On improved estimation of normal precision matrix and discriminant coefficients
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DOI：
10.1016/j.jmva.2005.11.006
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发表时间：
2006-08
影响因子：
1.6
通讯作者：
Hisayuki Tsukuma;Yoshihiko Konno
中科院分区：
文献类型：
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作者：
Hisayuki Tsukuma;Yoshihiko Konno
考虑关于二次损失函数的多元正态分布模型的精度矩阵的估计问题。最初用于各种损失函数的许多协方差估计器被修改以获得精度矩阵的替代估计器。结果表明，替代估计量在分析上比精度矩阵的无偏估计量具有更小的风险。通过对风险值的数值研究，表明新的估计量大大降低了风险。此外，我们还考虑了判别系数的估计问题，该问题在线性判别分析中出现，当假设两类均值不同但具有共同的协方差矩阵时，Fisher 线性判别函数被视为后验对数赔率。上述方法也适用于该问题，以获得二次损失函数下判别系数的改进估计量。此外，还进行了一项数值研究，以将一组替代方案的属性与判别系数的“无偏”估计量进行比较。
The problem of estimating the precision matrix of a multivariate normal distribution model is considered with respect to a quadratic loss function. A number of covariance estimators originally intended for a variety of loss functions are adapted so as to obtain alternative estimators of the precision matrix. It is shown that the alternative estimators have analytically smaller risks than the unbiased estimator of the precision matrix. Through numerical studies of risk values, it is shown that the new estimators have substantial reduction in risk. In addition, we consider the problem of the estimation of discriminant coefficients, which arises in linear discriminant analysis when Fisher's linear discriminant function is viewed as the posterior log-odds under the assumption that two classes differ in mean but have a common covariance matrix. The above method is also adapted for this problem in order to obtain improved estimators of the discriminant coefficients under the quadratic loss function. Furthermore, a numerical study is undertaken to compare the properties of a collection of alternatives to the “unbiased” estimator of the discriminant coefficients.