In:
Statistical Modelling, SAGE Publications, Vol. 13, No. 5-6 ( 2013-10), p. 431-457
Abstract:
In the setting of inference with two-step monotone incomplete data drawn from N d ( 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 T 2 -statistic, thereby enabling the construction of exact level ellipsoidal confidence regions for µ. By applying the equivariance of [Formula: see text] and [Formula: see text] the maximum likelihood estimators of µ and ∑, respectively, we show that the T 2 -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 T 2 -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.
Type of Medium:
Online Resource
ISSN:
1471-082X
,
1477-0342
DOI:
10.1177/1471082X13494611
Language:
English
Publisher:
SAGE Publications
Publication Date:
2013
detail.hit.zdb_id:
2053876-5
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