Introduced in 1937, the Pitman closeness criterion is one criterion for choosing between estimators of some population parameter. This criterion is based on the probability that one estimator produces an estimate that is closer to the parameter of interest than another competing estimator within the same class. Recently its use in the context of ordered data has been explored, for example for order statistics and record values. In this talk, I will discuss its use in progressive censoring.

In the first part of my talk, I will describe its use in finding an optimal progressive censoring scheme when the underlying distribution is exponential. Within this, we explicitly calculate the Pitman closeness probabilities and show that for some small sample sizes, the optimal progressive censoring scheme is the usual Type-II right censoring. We conjecture this to be the case for all sample sizes. We also present a general algorithm for the numerical computation of the Pitman closeness probabilities.

Following this, I will consider the case of two independent progressively Type-II censored samples. We begin with determination of Pitman closeness probabilities of order statistics from two independent samples to population quantiles. From there, we then consider the point prediction of a future progressively censored order statistic and discuss the determination of the closest progressively censored order statistic from the current sample according to the simultaneous closeness probabilities. For both these two-sample problems, explicit expressions are derived for the pertinent Pitman closeness probabilities, and then special cases are given as examples. For various censoring schemes, we also present numerical results for the standard uniform, standard exponential, and standard normal distributions. Finally, a distribution-free result for the median is obtained.