Wojciech Wójciak
supervisor: Jacek WesoĊowski
Sample allocation is one of the basic issues of survey sampling. It is a procedure of dividing the total sample among disjoint subsets of a finite population such as strata. The allocation procedure is called optimal because in a particular survey sampling design it produces the smallest variance for estimating a population total or mean of a given study variable. A thorough analysis of the literature shows that even for the generic scheme of stratified simple random sampling without replacement in each strata, the optimal sample allocation under lower and upper bounds restrictions imposed on sample sizes in strata remains an important problem which is not well understood and suffers from the lack of satisfactory algorithms.
The main research objective of this work is to solve the problem of optimum sample allocation under lower and upper bounds restrictions imposed on sample sizes in strata for various and important sampling schemes. The generic sampling scheme in this context is the stratified sampling with simple random sampling without replacement in strata. We plan to use and adopt tools and methods of convex optimization theory. The solution to the problem will be the set of so called optimality conditions, given as closed-form expressions, along with new efficient algorithms constructed on their basis. Such approach to the optimal allocation problem is unique.