28 Large-Sample Approximations to the Best Linear Unbiased Estimation and Best Linear Unbiased Prediction Based on Progressively Censored Samples and Some Applications N. Balakrishnan and C. R. Rao McMaster University, Hamilton, Canada Pennsylvania State University, University Park, PA Abstract: In this paper, we consider the situation where a life-testing exper- iment yields a Type-II progressively censored sample. We then develop large- sample approximations to the best linear unbiased estimators for the scale- parameter as well as for the location-scale parameter families of distributions. Large-sample expressions are also derived for the variances and covariance of these estimators. These results are used further to develop large-sample approx- imations to the best linear unbiased predictors of future failures. Finally, we present two examples in order to illustrate the methods of inference developed in this paper. Keywords and phrases: Progressive censoring, order statistics, life-testing, best linear unbiased estimation, best linear unbiased prediction, exponential distribution, extreme value distribution, Weibull distribution, Uniform distri- bution 28.1 Introduction Progressive Type-II censoring occurs when some live units are removed at the times of failure of a few units. Such a progressive Type-II censored sampling is certainly an economical way of securing data from a life-testing experiment, as compared to the cost of obtaining a complete sample. It also enables the observation of some extreme life-times while a conventional Type-II right cen- sored sampling will prohibit the observation of extreme life-times. Thus, pro- 431 S. Panchapakesan et al. (eds.), Advances in Statistical Decision Theory and Applications © Birkhäuser Boston 1997