Finite-sample inference with monotone incomplete multivariate normal data, III: Hotelling’s T2-statistic
Finite-sample inference with monotone incomplete multivariate normal data, III: Hotelling’s T2-statistic
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单调不完整多元正态数据的有限样本推理，III：Hotelling 的 T2 统计量
DOI：
10.1177/1471082x13494611
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发表时间：
2013
影响因子：
1
通讯作者：
D. Richards
中科院分区：
文献类型：
--
作者：
Megan M. Romer;D. Richards
在基于多元正态总体Nd（µ，∑）的两步单调不完全数据推断的情况下，我们得到了Hotelling’s t2统计量泛化的精确分布的随机表示，从而可以构造µ的精确水平椭球置信区域。利用µ和∑的极大似然估计量μ ^和Σ ^的等方差，证明了t2统计量在仿射变换下是不变的。此外，作为精确随机表示的结果，我们推导了t2统计量的累积分布函数的上界和下界。我们将这些结果应用于构建μ线性组合的同时置信区域，并将这些结果应用于分析由一组宾夕法尼亚州心脏病患者的胆固醇测量数据组成的数据集。
In the setting of inference with two-step monotone incomplete data drawn from Nd(µ, ∑), a multivariate normal population with mean µ and covariance matrix ∑, we derive a stochastic representation for the exact distribution of a generalization of Hotelling’s T2-statistic, thereby enabling the construction of exact level ellipsoidal confidence regions for µ. By applying the equivariance of μ ^ and Σ ^ , the maximum likelihood estimators of µ and ∑, respectively, we show that the T2-statistic is invariant under affine transformations. Further, as a consequence of the exact stochastic representation, we derive upper and lower bounds for the cumulative distribution function of the T2-statistic. We apply these results to construct simultaneous confidence regions for linear combinations of µ, and we apply these results to analyze a dataset consisting of cholesterol measurements on a group of Pennsylvania heart disease patients.