Impact of Censoring on Sample Variances in a Bivariate Normal Model

Suppose a bivariate normal random sample of size n is subjected to Type II censoring on one of the variates so that only a set of p order statistics and their concomitants are observed. For singly and symmetrically censored samples, we obtain close approximations to the distributions of sample variances of the observed order statistics and their concomitants by gamma distributions. We use simulation, method of maximum likelihood and moment matching techniques to express the gamma parameters involved as explicit functions of n and p, and in the case of concomitants, also the correlation coefficient. We examine the goodness-of-fit of these gamma approximations and the accuracy of the associated estimates of the percentiles of the two sample variances