DISCRIMINANT ANALYSIS WHEN A BLOCK OF OBSERVATIONS IS MISSING

HIE-CHOON CHUNG^{1} AND CHIEN-PAI HAN^{2}

1Department of Industrial and Information Engineering, Kwangju University, Kwangju 503-703, South Korea

2Department of Mathematics, University of Texas at Arlington, Arlington, TX76019, U.S.A.

(Received January 13, 1998; revised March 2, 1999)

Abstract. We consider the problem of classifying a p×1 observation into one of two multivariate normal populations when the training samples contain a block of missing observations. A new classification procedure is proposed which is a linear combination of two discriminant functions, one based on the complete samples and the other on the incomplete samples. The new discriminant function is easy to use. We consider the estimation of error rate of the linear combination classification procedure by using the leave-one-out estimation and bootstrap estimation. A Monte Carlo study is conducted to evaluate the error rate and the estimation of it. A numerical example is given to illustrate its use.

Key words and phrases: Block of missing observations, linear combination of two discriminant functions, linear combination classification, leave-one-out estimate, bootstrap estimate, Monte Carlo study.