On the LBI criterion for the multivariate one-way random effects model under non-normality

Solomon W. Harrar; Arjun K. Gupta

doi:10.1080/02331880500186185

On the LBI criterion for the multivariate one-way random effects model under non-normality

Solomon W. Harrar, Arjun K. Gupta

Dr. Bing Zhang Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

The asymptotic null distribution of the locally best invariant (LBI) test criterion for testing the random effect in the one-way multivariable analysis of variance model is derived under normality and non-normality. The error of the approximation is characterized as O(1/ n ). The non-null asymptotic distribution is also discussed. In addition to providing a way of obtaining percentage points and p -values, the results of this paper are useful in assessing the robustness of the LBI criterion. Numerical results are presented to illustrate the accuracy of the approximation.

Original language	English
Pages (from-to)	405-414
Number of pages	10
Journal	Statistics
Volume	39
Issue number	5
DOIs	https://doi.org/10.1080/02331880500186185
State	Published - Oct 1 2005

Keywords

Asymptotic expansion
LBI test
Multi-variate analysis of variance
Non-normality
Random effects model
Robustness
Variance components

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1080/02331880500186185

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abstract = "The asymptotic null distribution of the locally best invariant (LBI) test criterion for testing the random effect in the one-way multivariable analysis of variance model is derived under normality and non-normality. The error of the approximation is characterized as O(1/ n ). The non-null asymptotic distribution is also discussed. In addition to providing a way of obtaining percentage points and p -values, the results of this paper are useful in assessing the robustness of the LBI criterion. Numerical results are presented to illustrate the accuracy of the approximation.",

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N2 - The asymptotic null distribution of the locally best invariant (LBI) test criterion for testing the random effect in the one-way multivariable analysis of variance model is derived under normality and non-normality. The error of the approximation is characterized as O(1/ n ). The non-null asymptotic distribution is also discussed. In addition to providing a way of obtaining percentage points and p -values, the results of this paper are useful in assessing the robustness of the LBI criterion. Numerical results are presented to illustrate the accuracy of the approximation.

AB - The asymptotic null distribution of the locally best invariant (LBI) test criterion for testing the random effect in the one-way multivariable analysis of variance model is derived under normality and non-normality. The error of the approximation is characterized as O(1/ n ). The non-null asymptotic distribution is also discussed. In addition to providing a way of obtaining percentage points and p -values, the results of this paper are useful in assessing the robustness of the LBI criterion. Numerical results are presented to illustrate the accuracy of the approximation.

KW - Asymptotic expansion

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KW - Multi-variate analysis of variance

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KW - Random effects model

KW - Robustness

KW - Variance components

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On the LBI criterion for the multivariate one-way random effects model under non-normality

Abstract

Keywords

ASJC Scopus subject areas

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