Journal of Statistical Computation & Simulation Vol. 74, No. 6, June 2004, pp. 445–460 ROBUST DISCRIMINANT ANALYSIS USING WEIGHTED LIKELIHOOD ESTIMATORS AYANENDRANATH BASU a, *, SMARAJIT BOSE b,y and SUMITRA PURKAYASTHA b,z a Applied Statistics Unit and b Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Kolkata 700 108, India (Received 8 August 2002; In final form 23 July 2003) The procedures in traditional discriminant analysis suffer from serious lack of robustness under model misspecifications. Weighted likelihood estimators based on certain minimum divergence criteria have recently been shown (Markatou et al., 1998) to retain first order efficiency under the model while having attractive robustness properties away from it. In this paper, these estimators have been used to develop classifiers which are robust alternatives to Fisher’s discriminant analysis. Results of an extensive simulation study and some real data sets are presented to illustrate the usefulness of the proposed methods. Keywords: Discriminant analysis; Hellinger distance; Kernel density estimation; Minimum divergence; Robustness; Smoothing; Weighted likelihood estimators AMS 2000 Subject Classifications: 62H30, 62G35 1 INTRODUCTION Many optimal classical methods are derived under exact parametric models with no provision for any departure from the assumed model. Very often, however, the assumptions necessary for these methods are at most approximations to reality, and asymptotically efficient methods like the maximum likelihood can be severely affected under even moderate perturbations of the underlying model. Nonparametric methods, on the other hand, may exhibit significant loss in efficiency compared to optimal parametric methods, when the model is correct. Since in real life a small proportion of data contaminations are routine occurrences, it seems essential to construct estimators having full efficiency under the model and strong robustness properties away from it. In this paper we look at a procedure based on density based minimum divergence methods and investigate its applicability for the purpose of robust discriminant analysis. Several authors have tried to address the issue of robustness in discriminant analysis. Such studies can broadly be classified into two types. In one of these, robustness of linear and * E-mail: ayanbasu@isical.ac.in y E-mail: smarajit@isical.ac.in z Corresponding author. Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Kolkata 700 108, India; Fax: þ91-033-25773071=þ91-033-25776680; E-mail: sumitra@isical.ac.in ISSN 0094-9655 print; ISSN 1563-5163 online # 2004 Taylor & Francis Ltd DOI: 10.1080=00949650310001609458