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A Path Length Inequality for the Multivariate-t Distribution, With Applications to Multiple Comparisons

Melinda McCann and Don Edwards
Journal of the American Statistical Association
Vol. 91, No. 433 (Mar., 1996), pp. 211-216
DOI: 10.2307/2291397
Stable URL: http://www.jstor.org/stable/2291397
Page Count: 6
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A Path Length Inequality for the Multivariate-t Distribution, With Applications to Multiple Comparisons
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Abstract

This article presents a new inequality for the multivariate-t distribution, which implies a new method for multiple comparisons whose foundation rests on a recent inequality due to Naiman. The new method is promising in view of the fact that it utilizes information (estimator intercorrelations) ignored by the most widely used multiple comparison methods yet is not computationally prohibitive, requiring only the numerical evaluation of a single one-dimensional integral. In this article the validity of the new method in the normal-theoretic general linear model is established, and efficiency studies relative to the methods of Scheffé, Bonferroni, Šidák, and Hunter-Worsley are presented. The new method is shown to always improve on Scheffé's method. The new method is also shown to perform well; that is, to lead to a smaller critical point than its competitors, with low degrees of freedom. But the method is not as efficient as the Hunter-Worsley method for high degrees of freedom. In addition, the method appears to increase in relative efficiency as the number of comparisons increases relative to the rank of the correlation matrix of the estimators.

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