A Simple Method of Exact Optimal Sample Allocation Under Stratification with Any Mixed Constraint Patterns

• Activity Number: 616
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Survey Research Methods Section
• Author(s): Tommy Wright*+
• Companies: U.S. Census Bureau
• Keywords: Exact optimal allocation ; Mixed constraint patterns ; Neyman allocation ; Stratification

Abstract

Wright (2012) provides an exact optimal allocation of the fixed overall sample size n among H strata under stratified random sampling that minimizes the sampling variance of an estimator of a total subject to the constraint that the total sample size is n. The exact optimal allocation avoids the need to round the optimal sample sizes for the strata to integer values, as is the case with Neyman allocation. Neyman allocation with rounded integers does not always lead to the optimal allocation, that is, an allocation that minimizes the sampling variance subject to the constraint.

In this paper, we demonstrate that it is very easy to extend and generalize the result in Wright(2012) to the problem of finding an exact optimal allocation to minimize the sampling variance subject to the constraint that the total sample size is n and additional mixed constraint patterns which place stated upper U(h) and lower L(h) bounds on the sample size for stratum h, for h = 1, 2, ..., H. Avoiding the costly tendency to round up to ensure minimum sampling variance, the exact optimal allocation is especially useful in applications where H is very large and there are lower and upper size constraints