On the allocation of sample size in stratified sampling

Optimum Allocation of Sample Size and Prior Distributions: A Review

“…Let ;ij be the probability of inclusion of the jth unit of the ith stratum in the sample, j = 1, 2, ..., Nj; i = 1, 2, ..., k. As an estimator of the population total Y = EE Yij, consider the Horvitz-Thompson (1952) We call this the 0-optimum allocation. For this 0-optimum allocation we have a generalization of Rao's (1968) theorem the proof of which follows on the same lines as in Rao (1968) It is, however, not known from this under what conditions unstratified irPS sampling is still inferior to stratified irPS sampling when one deviates from the 0-optimum allocation. With this aim, Ramachandran and Rao (1974a) investigated whether stratified nPS sampling with various non-optimal allocations is likely to be worthwhile and whether it should at all be attempted in practice.…”

“…Note that for g = 2, b6 (g) = 0 and the allocation reduces to allocation proportional to X,. Elsewhere, the condition for the general case has been interpreted as the squares of the "corrected coefficients of variation" being equal in all strata and the results have been illustrated (Rao, 1968).…”

“…This problem was first considered by Hanurav (1965) and Rao (1968) for special cases of (1.1). Ericson (1965) studied the problem of optimum stratified sampling when prior information is taken to be expressible in the form of a multivariate Normal prior distribution.…”

Stratified simple random sampling and prior distributions

“…[14], we have that the do optimum n, will be proportional to N,m if 32, X,}N~ -~ is proportional to ~ and if this condition J is satisfied, we have that ni,~opt= nN~ai/E N~ai , and the expected variance corresponding to this J~ optimum allocation is given by…”

“…The justification for the assumption that the unknown proportionate values of S~'s are usually not quite different from the proportionate values of the known ~'s was examined in the light of an a priori distribution by Hanurav [10], which was further studied by Rao, T. J. [14] and Vijayan, K. [17] among others, and it is pursued further in this paper.…”