Statistical inference for censored bivariate normal distributions based on induced order statistics

Abstract

For a censored sample from a bivariate normal distribution consisting of the first k of n order statistics of one variable and the induced order statistics of the other variable, the maximum likelihood estimators of the parameters and the associated large sample co-variance matrix are derived. The likelihood ratio test for independence is also given and its power properties studied. These methods are useful in selection problems or in life testing situations in which concomitant variates are observable only for the uncensored primary variates.