OPTIMALITY ROBUSTNESS OF CLASSIFICATION INTO ONE OF TWO MULTIVARIATE POPULATIONS WITH UNKNOWN LOCATIONS AND EQUAL SCALE MATRICES

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  • Hara Takahiko
    Institute of Socio-Economic Planning, University of Tsukuba

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  • Optimality Robustness of Classification

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Abstract

This paper is concerned with a multiple decision problem having location slippage hypotheses in a multivariate regression model. The underlying distribution is assumed to be any member of a class of elliptically contoured distributions. We propose a decision rule based on a generalized version of the sample Mahalanobis squared distance, and show that the decision rule is admissible and minimax for the multiple decision problem. Our multiple decision problem includes the problem of classifying a future observation into one of two multivariate elliptically contoured populations with unknown locations and unknown but equal scale matrices. This is an extension of Kudô (1959) and Das Gupta (1965) where the underlying distribution was normal. Our results indicate that their classification rule is robust in the sense that the optimal properties of their classification rule are carried over to non-normal distributions. Kariya and Sinha (1985, 1989) call this optimality robustness.

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