Finite-sample inference with monotone incomplete multivariate normal data, III: Hotelling's T2-statistic

Megan M. Romer, Donald St P. Richards

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

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 μ̂ and Σ̂, 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.

Original languageEnglish (US)
Pages (from-to)431-457
Number of pages27
JournalStatistical Modelling
Volume13
Issue number5-6
DOIs
StatePublished - Oct 2013

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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