Bayes and Minimax Procedures in Sampling From Finite and Infinite Populations--I

Abstract

Some of the sampling methods and the methods of estimation usually employed in sample surveys are considered in terms of loss and risk functions. The loss function is taken as the sum of two components, one proportional to the square of the error of the estimate and the other proportional to the cost of obtaining the sample. Consideration is given to the problem of the allocation of the total sample size and only non-sequential estimates are discussed. As the loss function is convex and of finite expectation in each case, only non-randomized estimates are considered, since Hodges and Lehmann [5] have shown that under these conditions the class of non-randomized estimates is essentially complete. Only simple random sampling and stratified sampling methods are discussed in this part, the ratio, regression and sub-sampling methods will be discussed in subsequent parts.