Discriminant Analysis When the Initial Samples are Contaminated

This paper investigates one aspect of the robustness of Fisher's linear discriminant function-robustness against contamination in the initial samples. Asymptotic results are derived for normal location contamination and for normal scale contamination with the contaminating covariance matrix a multiple of the uncontaminated population covariance matrix. It is shown that when the prior probabilities of the two underlying populations are equal, scale contamination of the initial samples has no effect on our ability to make correct classifications. When the prior probabilities of the two populations are unequal, scale contamination can have a harmful effect. Location contamination can be even more harmful than scale contamination. Small sample results are presented for the case of scale contamination with equal prior probabilities. Finding that for small samples, Fisher's LDF may perform very poorly when the initial samples are scale contaminated, three types of "robust discriminant functions" are proposed as alternatives to Fisher's LDF. The three types of dis-criminant functions are evaluated for various combinations of parameters (sample size, distance between the underlying populations, amount of contamination, type of contamination). It is found that for mild contamination , Fisher's LDF performs as well as the "robust procedures." For more severe contamination, a Type I LDF, formed from Fisher's LDF by replacing Xl' x 2 ' and S by robust estimates of location and scale, improves our ability to discriminate. Adviser Reader Reader ACKNOWLEDGMENTS The author wishes to express her appreciation for the assistance of her advisor, Dr. P. A. Lachenbruch, who suggested the problem and who provided gUidance throughout the research. In addition, she would like to thank the other members of her committee, Dr. helpful criticisms and suggestions. She also wishes to thank her husband, Yahia, for his encouragement throughout her studies and her daughter, Wendy, who was born in the middle of the writing of this dissertation, for her patience during the first six months of her life. Finally, she wishes to express her thanks to Mrs. Gay Hinnant for her excellent typing of this manuscript.