Wojciech Wójciak
supervisor: Jacek WesoĊowski
The minimum sample size allocation problem in stratified sampling is one of the basic issues of modern survey sampling methodology. It is formulated as the determination of the fixed strata sample sizes that minimize total sample size, under assumed level of the variance of the stratified pi-estimator. In this work, we derive so called optimality conditions for the minimum sample size allocation problem under added one-sided upper bounds constraints imposed on strata sample sizes. This allocation problem will be considered here in the context of some general stratified sampling scheme that includes simple random sampling without replacement design within strata as a special case. Based on the established optimality conditions, we create a new algorithm, termed LrNa, that solves the allocation problem defined above. This new algorithm has its origin in popular recursive Neyman allocation procedure, or rNa, that is used to solve classical optimal sample allocation problem (i.e. minimization of the pi-estimator's variance under fixed total sample size) with only one-sided upper bounds constraints imposed on strata sample sizes. Ready-to-use R-implementation of the LrNa is available on CRAN repository at https://cran.r-project.org/web/packages/stratallo.