Bayesian Cramer-Rao Lower Bound of Variances under Ranked Set Sampling*

Abstract

Ranked set sampling (RSS) is regarded as a substitute of simple random sampling (SRS). Under SRS, obtained samples are onlyindependent, whereas in cases of balanced RSS, observations are independent order statistics. This paper presents a method to calculate the Bayesian Cramer Rao (BCR) bound when the statistical model is based on independent order statistics. This bound is also compared with independent simple random samples. In context of order samples where this classical Cramer Rao (CR) bound is hard to evaluate, this study presents a closed-form expression of a BCR bound. The efficiency in BCR bound due to independent order observations as compared to independent samples, is procure on the basis of theoretical and simulation results. Through this one can evaluate the significance of using independent order statistics as compare to independent samples for the gains in accuracy to estimate the parameters and reduction in required sample size. The procured results demonstrate that BCR bound based on independent order statistics is more compact, efficient observational economic than SRS based bound ofestimator.