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Rectangular Confidence Regions for the Means of Multivariate Normal Distributions
Abstract
For rectangular confidence regions for the mean values of multivariate normal distributions the following conjecture of 0. 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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Research works printed but not linked: 11
- Anderson, T. W. “The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities,”. Proceedings of the American Mathematical Society. Vol. 6, pp.170–76. · doi:10.2307/2032333
- Anderson T. W., 1958, An Introduction to Multivariate Statistical Analysis
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- 10.1080/01621459.1965.10480814 · doi:10.1080/01621459.1965.10480814
- Dunnett C. W., 1955, Biometrika, 42, 258, 10.1093/biomet/42.1-2.258 · doi:10.1093/biomet/42.1-2.258
- 10.1214/aoms/1177704004 · DOI
- 10.1080/01621459.1955.10501257 · DOI
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- Slepian D., 1962, Bell System Technical Journal, 41, 463, 10.1002/j.1538-7305.1962.tb02419.x · DOI · Paper page
Cited by
Pfeffer, M. A., McMurray, J. J. V., Velazquez, E. J., Rouleau, J.-L., Køber, L., Maggioni, A. P., Solomon, S. D., Swedberg, K., Van de Werf, F., White, H., et al. (2003) · New England Journal of Medicine · doi:10.1056/nejmoa032292 · Cited by 2,471
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Li, J., & Ji, L. (2005) · Heredity · doi:10.1038/sj.hdy.6800717 · Cited by 1,458
Do multiple outcome measures require p-value adjustment?
Feise, R. J. (2002) · BMC Medical Research Methodology · doi:10.1186/1471-2288-2-8 · Cited by 1,299
Bretz, F., Hothorn, T., & Westfall, P. (2016) · doi:10.1201/9781420010909 · Cited by 1,233
Metadata
- Authors
- Šidák, Z.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1967-06
- Volume
- 62
- Issue
- 318
- Pages
- 626-633
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2037586880
- Cited by
- 2,639
- References
- 0
- FWCI
- 6.99
- Type
- journal article
- Language
- en
- Open access
- closed
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