Estimation of the parameters for a multivariate normal distribution when one variable is dichotomized

Abstract

The problem discussed is the estimation of the parameters of a multivariate normal distribution using a sample from a dichotomization of this distribution, with the emphasis on large-sample distributions of the estimators. The usual Newton's method is adapted to the present situation for the solution of the likelihood equations. The various expressions which are derived are illustrated by a problem in educational testing. Results extend those of Maritz (1953) and Tate (1955).