Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series B, Pt. 2, 246--268

ROBUST M-ESTIMATION IN DISCRIMINANT ANALYSIS

By

INDRANI BASAK Altoona College, Penn State Altoona

SUMMARY. Robust M-estimation procedures for relevant parameters of discriminant analysis are developed. The optimal robust M-estimators for discriminant function coefficients, Mahalanobis' D2 and misclassification probabilities are obtained. These optimal robust estimators do not generally have breakdown point of 0.5. Other robust estimators for discriminant function coefficients, Mahalanobis' D2 and misclassification probabilities belonging to one special class of estimators are proposed. It is shown that certain estimators belonging to this class have breakdown point 0.5. However, this optimality in breakdown point is achieved by a compromise in efficiency.

AMS (1991) subject classification.62H30, 62H12.

Key words and phrases. Discriminant function coefficients, Mahalanobis' distance, misclassification probability, M-estimators, influence functions, breakdown point, optimal robust M-estimators.

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