A Simple and General Algorithm for Exact Optimal Sample Allocation That Is More Efficient Than Neyman Allocation

• Activity Number: 606
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Survey Research Methods Section
• Author(s): Tommy Wright*
• Companies: U.S. Census Bureau/Center for Statistical Research & Methodology
• Keywords: Exact optimal allocation ; Mixed constraint patterns ; Neyman allocations ; Stratification

Abstract

Neyman allocation of the sample under stratified random sampling is among the top major advances and most widely used methods in probability sampling theory because it minimizes sampling variance. Unfortunately, (1) Neyman allocation does not usually yield integer solutions; (2) rounding to integers generally does not guarantee minimum sampling variance unless the sample size is increased; and (3) it can result in a sample size n_h for stratum h that exceeds the overall size of the stratum N_h. This paper presents simple exact optimal allocation algorithms that yield integer solutions which minimize the sampling variance and avoid the possibility of calculating n_h where n_h > N_h.

The exact optimal allocation Algorithm III is especially useful in applications where the number of strata is very large and there are minimum and maximum size constraints on the allocated sample sizes n_h, as is the case with the Census Bureau's Service Annual Survey of firms which has 391 primary sampling strata and over 3,500 substrata.

We show a simple decomposition of sampling variance that reveals why the algorithms always work in finding the optimum allocation.