Computing Optimal Strata Bounds Using Dynamic Programming

• Activity Number: 507
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Consulting
• Author(s): Eric Miller*+
• Companies: Summit Consulting
• Keywords: Dynamic Programming ; Stratified Random Sampling

Abstract

Stratification is a sampling design that can improve efficiency. It works by first partitioning the population into homogeneous subgroups and then performing simple random sampling within each group. For a continuous variable, stratification involves determining strata boundaries. Holding the number of strata fixed, a reduction in the width of a given stratum reduces its associated variance at the expense of the variances from the other strata. Dynamic programming provides a method for simultaneously minimizing all of the strata variances by determining optimal strata boundaries.

This presentation describes a method for calculating optimal strata bounds that practitioners can use to quickly and easily partition the sample. The proposed method operationalizes the variance minimization technique developed by Khan, Nand, and Ahmad (2008, Survey Methodology 34: 205-214). The user first chooses a known probability distribution that approximates the stratification variable. Parameter estimates are then generated from the data and goodness of fit statistics are used to assess the quality of the approximation. Several illustrative examples will be provided.