Classification and Estimation of Several Multiple Regressions

Abstract

Two problems, classifying an individual into one of several populations and estimating the regression in that population, are simultaneously treated as one problem. This can be viewed as a problem of a missing observation on a categorical variable. When all variables are jointly distributed multivariate normal, the maximum likelihood solution is the intuitively appealing one: classify the individual using the usual likelihood ratio procedure, then estimate the regression using the observations from the selected population.