Mathematics and Statistics Vol. 11(4), pp. 676 - 684
DOI: 10.13189/ms.2023.110409
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Optimal Stochastic Allocation in Multivariate Stratified Sampling

Mahfouz Maha I. ^1,*, Rashwan Mahmoud M. ², Khadr Zeinab A. ^2
1 National Centre for Social and Criminological Research, Egypt
² Department of Statistics, Faculty of Economics and Political Sciences, Cairo University, Egypt

ABSTRACT

Optimal allocation of stratified sample is obtained either by minimizing the variance of the sample estimate for a fixed total cost of the survey or the total cost of survey for the fixed precision of the estimate. Actually, the survey cost and the variance of the estimate move in opposite directions, that is minimizing any of them results in increasing the other. Moreover, in practice, due to the uncertainty in the population data, the variances as well as the costs should be treated as random variables. In this paper, a multivariate optimal stochastic compromise allocation is proposed using multi-objective mathematical programming model that simultaneously minimizes both of the total cost of the survey as well as the individual variances of the overall stratified mean of each of the characteristics of interest. The proposed Stochastic Programming model is to be solved using the Chance-Constrained Programming technique. The proportional increase in the variance of the estimator under the optimum variance and under the optimum cost is set as a constraint and is upper-bounded by a pre-determined quantity. Simulation-based comparative study is conducted to assess the performance of the proposed allocation versus other optimal allocation techniques. Based on the criteria used for comparison, the findings show that the suggested model produced the highest efficient estimators with the highest precision, and efficient allocation of the sample size to the strata that accounts for the differences in the strata sizes and the variation within strata.

KEYWORDS
Stratified Sampling Allocation, Optimal Allocation, Multivariate Optimal Allocation, Compromise Allocation, Weighted Goal Programming, Stochastic Allocation

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Mahfouz Maha I. , Rashwan Mahmoud M. , Khadr Zeinab A. , "Optimal Stochastic Allocation in Multivariate Stratified Sampling," Mathematics and Statistics, Vol. 11, No. 4, pp. 676 - 684, 2023. DOI: 10.13189/ms.2023.110409.

(b). APA Format:
Mahfouz Maha I. , Rashwan Mahmoud M. , Khadr Zeinab A. (2023). Optimal Stochastic Allocation in Multivariate Stratified Sampling. Mathematics and Statistics, 11(4), 676 - 684. DOI: 10.13189/ms.2023.110409.