1 A NONPARAMETRIC MULTICLASS PARTITIONING METHOD FOR CLASSIFICATION by SAUL BRIAN GELFAND

c classes are characterized by unknown probability distributions. A data sample containing labelled vectors from each of the c classes is available. The data sample is divided into test and training samples. A classifier is designed based on the training sample and evaluated with the test sample. The classifier is also evaluated based on its asymptotic properties as sample size increases. A multiclass recursive partitioning algorithm which generates a single binary decision tree for classifying all classes is given. The algorithm has the same desirable statistical and computational properties as Friedman's (1977) 2-class algorithm. Prior probabilities and losses are accounted for. A tree termination algorithm which terminates binary decision trees in a statistically optimal manner is given. GorT-don and Olshen's (1978) results on the asymptotic Bayes risk efficiency of 2-class recursive partitioning algorithms are extended to the c-class case and applied to the combined partitioning/termination algorithm. Asymptotic efficiency and consistent risk estimates are obtained with independent test and training sequences. 3 ACKNOWLEDGEMENT I would like to thank Professor Sanjoy Mitter for his intellectual and financial support throughout the course of this research. I would also like to acknowledge Don Gustafson whose ideas contributed heavily to the initial phase of the work.