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Rectangular Confidence Regions for the Means of Multivariate Normal Distributions

Zbynek Sidak
Journal of the American Statistical Association
Vol. 62, No. 318 (Jun., 1967), pp. 626-633
DOI: 10.2307/2283989
Stable URL: http://www.jstor.org/stable/2283989
Page Count: 8
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Rectangular Confidence Regions for the Means of Multivariate Normal Distributions
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Abstract

For rectangular confidence regions for the mean values of multivariate normal distributions the following conjecture of O. J. Dunn [3], [4] is proved: Such a confidence region constructed for the case of independent coordinates is, at the same time, a conservative confidence region for any case of dependent coordinates. This result is based on an inequality for the probabilities of rectangles in normal distributions, which permits one to factor out the probability for any single coordinate.

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