A Note on the Best Linear Unbiased Estimation Based on Order Statistics

Best linear unbiased estimators of location and scale parameters based on order statistics (from either complete or Type-II censored samples) are usually illustrated with exponential and uniform distributions. But the derivations in these two cases involve the explicit inverse of a diagonal matrix of Type 2 and extensive algebraic manipulations. In this note we present a simple method of derivation of these results that we feel will assist students in learning this method of estimation better. Furthermore, we use this simple approach to show some interesting properties of best linear unbiased estimators in the case of exponential distributions.