A New Power Allocation Method with a Nonlinear Cost Constraint in Stratified Random Sampling

Abstract

When
 the population is heterogeneous, stratified random sampling is generally
 preferred for estimation the population parameters. There are a lot of sample
 allocation methods in stratified random sampling. However, most of sample
 allocation methods ignore the selection cost or assume the selection cost as equal
 in all strata. Bankier also suggested a power allocation method without
 considering the cost function [1]. However, in real life applications, it is
 very rare to come across such cases. Therefore, it would be more realistic to
 take the cost into account for allocation procedures. In this study, a new
 power allocation method is proposed by taking into account a non-linear cost
 function constraint in Bankier’s method. The Neyman allocation and square root
 allocation results are also obtained by using this new allocation method. The
 performance of the proposed method is examined for different model parameters and
 their different cases using data from 2012 Structural Business Survey of TURKSTAT.