Optimum Stratification: A Mathematical Programming Approach

Abstract

The probelm of determining the optimum strata boundaries, when the main study variable is used as stratification variable and a stratified sample, using Neyman allocation (for a fixed total sample size) is to be selected to estimate the population mean (or total), is formulated as a mathematical programming problem (MPP). It has been shown that with some modification this MPP may be converted into a multistage decision problem that could be solved using dynamic programming technique. Two numerial examples are also presnted to illustrate the computational details.

Multivariate Multi-Objective Allocation in Stratified Random Sampling: A Game Theoretic Approach

“…For the outer segment of model (7), we can use any suitable goal programming technique discussed in ([22, 23, 28], [29–31], [34] and [35]). The above programme Eq (7) can be expressed as a Weighted Goal Programming (WGP) model as; where are sum of optimal Adversary’s objectives for stratum 1 and stratum 2, respectively.…”

Designing stratified sampling in economic and business surveys

“…Substituting this value of x h−1 , the recurrence relations (19) and (20) are used to solve the MPP (40), which are reduced as follows:…”

“…This approach was also used by Lavallée [26,27] for determining the OSB which would divide the population domain of two stratification variables into distinct subsets such that the precision of the variables of interest is maximized. Khan et al [19][20][21][22] and Nand and Khan [32] also use Downloaded by [New York University] at 05:44 02 August 2015 dynamic programming technique for determining the OSB when the frequency function of the survey variable is known.…”

Computing optimal stratum boundaries for multivariate surveys

“…Substituting equations (16) and (17) into MPP (15) and solving (via a computer program) it by using the DP technique over compromise distance d = max(var1, var2) − min(var1, var2) = 3.7360 − −3.6734 = 7.4094 with the initial value of x 0 = 0 gives the standardized OSB. To get the OSB for individual variables, it is first shifted appropriately (adding the minimum of that variable) since the initial value is 0.…”