Stratified simple random sampling and prior distributions
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The problem of stratification with proportional and optimum allocations in the case of simple random sampling has been examined in the light of an appropriate super-population model and a formal proof has been provided here for arranging the auxiliary character in increasing order of magnitude for stratification in the case of proportional allocation and also it is shown here that the same may not be necessary in the case of optimum allocation. However, if the coefficient of variation with respect to the auxiliary variate is same in each stratum the necessity of arraging the auxiliary character in increasing order of magnitude for stratification is established. The results are illustrated with respect to empirical examples. Also, some comparisons among different estimators have been made under the super-population model.
KeywordsStratified simple random sampling stratification mis-stratification: arranging the auxiliary character in the increasing or decreasing order of magnitude prior distributions, PPS sampling allocation of sample size to strata
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