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Simultaneous confidence intervals for umbrella contrasts of normal means
Year:
1994
Authors :
Genizi, Abraham
;
.
Marcus, Ruth
;
.
Volume :
17
Co-Authors:
Marcus, R., Agricultural Research Organization, Bet Dagan, Israel
Genizi, A., Agricultural Research Organization, Bet Dagan, Israel
Facilitators :
From page:
393
To page:
407
(
Total pages:
15
)
Abstract:
Two procedures for obtaining simultaneous confidence intervals for "umbrella" contrasts of normal means of the form Σciμi, where c1 ≤ ⋯ ≤ ch ≥ ⋯ ≥ ck and Σci = 0, are described. One procedure employs critical values of the likelihood ratio statistic proposed by Shi (1988) for testing homogeneity of normal means against an umbrella ordering, HU,h: μ1 ≤ ⋯ ≤ μh ≥ ⋯ ≥ μk), with h known. The second employs critical values of the statistics μh - min(μ1, μk), where {μi} are the maximum likelihood estimators of {μi under HU,h. The null distribution of the statistic is investigated by the Monte Carlo technique, and some percentiles are provided. The interval lengths obtained by these procedures are compared for different types of umbrella contrasts. Improved confidence bounds are generated when the means satisfy an umbrella ordering. © 1994.
Note:
Related Files :
Contrast with restricted coefficients
Isotonic regression
Maximum likelihood estimators
Order restricted tests
Umbrella ordering
Show More
Related Content
More details
DOI :
10.1016/0167-9473(94)90019-1
Article number:
Affiliations:
Database:
Scopus
Publication Type:
article
;
.
Language:
English
Editors' remarks:
ID:
22529
Last updated date:
02/03/2022 17:27
Creation date:
16/04/2018 23:52
Scientific Publication
Simultaneous confidence intervals for umbrella contrasts of normal means
17
Marcus, R., Agricultural Research Organization, Bet Dagan, Israel
Genizi, A., Agricultural Research Organization, Bet Dagan, Israel
Simultaneous confidence intervals for umbrella contrasts of normal means
Two procedures for obtaining simultaneous confidence intervals for "umbrella" contrasts of normal means of the form Σciμi, where c1 ≤ ⋯ ≤ ch ≥ ⋯ ≥ ck and Σci = 0, are described. One procedure employs critical values of the likelihood ratio statistic proposed by Shi (1988) for testing homogeneity of normal means against an umbrella ordering, HU,h: μ1 ≤ ⋯ ≤ μh ≥ ⋯ ≥ μk), with h known. The second employs critical values of the statistics μh - min(μ1, μk), where {μi} are the maximum likelihood estimators of {μi under HU,h. The null distribution of the statistic is investigated by the Monte Carlo technique, and some percentiles are provided. The interval lengths obtained by these procedures are compared for different types of umbrella contrasts. Improved confidence bounds are generated when the means satisfy an umbrella ordering. © 1994.
Scientific Publication
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