A Bayesian Approach to Two-Stage Sampling.
Final rept. 1 May 72-1 Jan 76,
MICHIGAN UNIV ANN ARBOR DEPT OF STATISTICS
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In several previous papers, the author has shown that various standard sampling designs are optimal in a Bayesian sense under corresponding classes of prior distributions on the N-dimensional vector of unknown characteristics of the N elements of a finite population. In this manner a Bayesian interpretation of simple random sampling, stratified random sampling, and of various ratio and regression estimators have been given. In the present report this work is extended to two-stage balanced sampling. Additionally, a simple result on a representation of finitely exchangeable discrete random variables is given which gives a slight generalization of a seemingly little-known result of de Finetti. Also a general tie between Bayes posterior means and traditional WLSEs and BLUEs is obtained, generalizing previous results given by the author. Author
- Statistics and Probability