Sankhya: The Indian Journal of Statistics

1997, Volume 59, Series A, Pt. 1, 74-87

A GENERAL DECISION RULE FOR DIMENSION IN THE CONTEXT OF MANOVA

By

ANINDYA K. DE, Purdue University, West Lafayette

And

JAYANTA K. GHOSH, Indian Statistical Institute, Calcutta

SUMMARY. It is often of interest to identify a linear structural relationship among the mean vectors in the context if Multivariate Analysis of Variance (MANOVA). In this paper we have generalised the results of De and Ghosh (1994) for the bivariate case to a d-variate case for d > 2. We have exhibited a Bayes solution for populations of arbitrary dimension and also derived a useful approximation which could be used in practice. As in the bivariate case, the Bayes rule closely resembles the ad hoc rule introduced in De and Ghosh (1994) which was shown to have good frequentist properties. A simulation study was carried out to compare the performance of the proposed rules.

AMS (1991) subject classification. 62C10, 62F15, 62J10

Key words and phrases. MANOVA, decision rule for dimension, approximate Bayes.

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