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

Megan M. Romer, Donald Richards

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 1 2013

Fingerprint

Hotelling's T2
Multivariate Normal
Stochastic Representation
Statistic
Monotone
Confidence Region
Equivariance
Cholesterol
Normal Population
Exact Distribution
Incomplete Data
Cumulative distribution function
Maximum Likelihood Estimator
Covariance matrix
Affine transformation
Linear Combination
Upper and Lower Bounds
Invariant
Hotelling
Finite sample

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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Finite-sample inference with monotone incomplete multivariate normal data, III : Hotelling's T2-statistic. / Romer, Megan M.; Richards, Donald.

In: Statistical Modelling, Vol. 13, No. 5-6, 01.10.2013, p. 431-457.

Research output: Contribution to journalArticle

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