ABSTRACT
In this chapter we consider parameter estimation in multivariate normal distributions from samples that may be truncated or censored with respect to one of the variables. Samples of this type arise when acceptance or screening procedures imposed on one variable eliminate certain sample specimens from further observation with respect to other variables. In regression or correlation studies, we may be concerned with predictions of success as measured by one or more variables from information provided by an acceptance examination score. Low-scoring candidates are eliminated and do not receive success scores. A manufacturer might wish to correlate physical characteristics such as weight, hardness, density, size, etc., with one or more performance characteristics such as life-span, operating costs, sales volume, or other characteristic for which observations are available only on accepted items. The determination of means, variances, and correlation coefficients from samples of these types poses a broad class of estimation problems, some of which are quite complex. Here our concern is limited to samples from a p-dimensional multivariate normal distribution where truncation and/or censoring applies to only a single screening (acceptance) variable.
