Calculations of level probabilities for normal random variables with unequal variances with applications to Bartholomew's test in unbalanced one-way models.
Calculations of level probabilities for normal random variables with unequal variances with applications to Bartholomew's test in unbalanced one-way models.
An effective procedure is presented to compute the level probabilities under simple order of independent normal random variables with unequal variances. These level probabilities have an application in the unbalanced one-way layout for comparing k treatment effects where Bartholomew (1959. Biometrika 48, 325–332, 1961a. J. Roy. Statist. Soc. Ser. B 23 239–281, 1961b. Biometrika 48, 325–332) proposed the likelihood ratio test for testing the homogeneity of the treatment effects against the simply ordered alternative hypothesis. Although there is some literature showing that Bartholomew's test has good properties, its null distribution for the unbalanced model has been difficult to calculate except for small k. The calculation of the level probabilities allows the computation of the p-values of Bartholomew's test for unbalanced models.
isotonic estimation, likelihood ratio test, monotone contrast, orthant probability, orthoscheme probability, simply ordered alternative, simultaneous confidence intervals
17-32
Miwa, Tetsuhisa
cb4e7293-e076-437a-b31c-b5dd6c6a3b4a
Hayter, A.J.
55bd07a5-db1d-4d3d-8c87-b307485420d9
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
2000
Miwa, Tetsuhisa
cb4e7293-e076-437a-b31c-b5dd6c6a3b4a
Hayter, A.J.
55bd07a5-db1d-4d3d-8c87-b307485420d9
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
Miwa, Tetsuhisa, Hayter, A.J. and Liu, Wei
(2000)
Calculations of level probabilities for normal random variables with unequal variances with applications to Bartholomew's test in unbalanced one-way models.
Computational Statistics and Data Analysis, 34 (1), .
(doi:10.1016/S0167-9473(99)00075-4).
Abstract
An effective procedure is presented to compute the level probabilities under simple order of independent normal random variables with unequal variances. These level probabilities have an application in the unbalanced one-way layout for comparing k treatment effects where Bartholomew (1959. Biometrika 48, 325–332, 1961a. J. Roy. Statist. Soc. Ser. B 23 239–281, 1961b. Biometrika 48, 325–332) proposed the likelihood ratio test for testing the homogeneity of the treatment effects against the simply ordered alternative hypothesis. Although there is some literature showing that Bartholomew's test has good properties, its null distribution for the unbalanced model has been difficult to calculate except for small k. The calculation of the level probabilities allows the computation of the p-values of Bartholomew's test for unbalanced models.
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Published date: 2000
Keywords:
isotonic estimation, likelihood ratio test, monotone contrast, orthant probability, orthoscheme probability, simply ordered alternative, simultaneous confidence intervals
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Statistics
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Local EPrints ID: 30101
URI: http://eprints.soton.ac.uk/id/eprint/30101
ISSN: 0167-9473
PURE UUID: 4b33fb87-51f1-4008-b294-08c503f4d6e0
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Date deposited: 20 Jul 2006
Last modified: 16 Mar 2024 02:42
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Author:
Tetsuhisa Miwa
Author:
A.J. Hayter
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