Optimal Stochastic Allocation in Multivariate Stratified Sampling / By Maha Ismail Mahfouz Ismail; Supervised by Prof. Zeinab Ali Abd El-Aziz Khadr, Dr. Mahmoud Mostafa Rashwan, Dr. Mohammed Abd El-Ghani Ramadan

Thesis (Ph.D)-Cairo University, 2023.

Bibliography: pages 70-74.

The allocation of stratified sampling is the problem of determining the number of
observations to be selected from each stratum. Many authors introduced optimization-based
allocation techniques that utilize the mathematical programming approach to obtain an optimal
allocation that optimizes certain objective function under some constraints. The main challenge
of the optimal allocation is the compromise between the two conflicting objectives of the cost of
the survey and the precision of the estimates. In the literature, the optimal allocations obtained
either minimize variation for the estimates under a given cost of the survey or minimize cost at a
given precision level of the estimates. In multivariate surveys, the optimal allocation for one
characteristic may result in a loss of the precision of the estimates of the other characteristics.
This study proposes a multivariate optimal compromise allocation using a multi-objective
mathematical programming model that simultaneously minimizes the total cost of the survey and
the variation of the overall stratified mean of all of the characteristics of interest. The
proportional increase in the estimator's variance due to minimizing the variance compared to the
estimator's variance due to minimizing the cost is set as a constraint and is upper-bounded by a
pre-determined quantity. Weighted Goal Programming is adopted as a solution technique, which
has the flexibility of introducing different weights to the different goals according to the decision
maker’s requirements. Integer programming is used to guarantee integer values for the optimal
allocation.
However, in practice, because the population data are usually unknown and are estimated
under uncertainty, thus, their sample estimates should be better treated as random variables.
Therefore, the proposed model introduces another form implementing a Stochastic Programming
model that is solved using the Chance-Constrained Programming technique. A simulation-based
comparative study is conducted to assess the performance of the proposed allocation models
versus other allocation techniques. The results show that, according to the criteria used for
comparison, the proposed models produced estimators with the highest precision in most of the
cases.

الهدف الرئيسى من هذه الدراسة هو تقديم أسلوب برمجة متعدد الأهداف يهدف للتعامل مع مشكلة التخصيص في المعاينة العشوائية الطبقية عن طريق تصغير كل من تباين مقدر متوسط المجتمع، بالإضافة إلى الميزانية المستخدمة فى آن واحد. وتم تقديم صورة أخرى من النموذج فى شكل برمجة إحتمالية مع افتراض أن التباين وبعض بنود الميزانية هى متغيرات عشوائية تتبع توزيع احتمالى معين. بالإضافة إلى ذلك، يتم مقارنة النماذج المُقترحة مع نماذج أخرى قُدمت فى الدراسات السابقة من خلال دراسة محاكاة. ويتم تقييم أداء النماذج باستخدام ثلاثة معايير لقياس كفاءة النماذج فى الحصول على مقدرات المجتمع. و بناءاً على هذه المعايير، أفادت النتائج التى تم التوصل اليها أن النماذج المقترحة كانت الأكثر كفاءة في الحصول على مقدرات المتوسطات داخل الطبقات و ذلك في معظم الحالات.

Issued also as CD

Text in English and abstract in Arabic & English.