Revisiting Best Linear Unbiased Estimation of Location-Scale Parameters Based on Optimally Selected Order Statistics Using Compound Design

We introduce here the compound optimal design strategy to determine the Best Linear Unbiased Estimates (BLUEs) of location and scale parameters based on suitably chosen few order statistics. It is shown that the linear estimates of the parameters from any location-scale distribution, based on few optimally chosen ranks, obtained from the compound optimal design criterion is indeed the BLUE. Further extension of the strategy to Asymptotically Best Linear Unbiased Estimates (ABLUEs) is also discussed. The validation of the proposed strategy is justified through a numerical study for normal, Laplace and logistic distributions. Finally, a real-life data set is analyzed to illustrate the proposed strategy.