Marcus, R., Agricultural Research Organization, Bet Dagan, Israel

Genizi, A., Agricultural Research Organization, Bet Dagan, Israel

Genizi, A., Agricultural Research Organization, Bet Dagan, Israel

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.

Simultaneous confidence intervals for umbrella contrasts of normal means

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Marcus, R., Agricultural Research Organization, Bet Dagan, Israel

Genizi, A., 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.

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