Stratification of a Sampling Frame with Auxiliary Data Into Piecewise Linear Segments by Means of a Genetic Algorithm

• Activity Number: 243
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Government Statistics
• Author(s): Joseph James Barth*+ and Yang Cheng
• Companies: U.S. Census Bureau and U.S. Census Bureau
• Keywords: Piecewise linear fit ; genetic algorithm ; survey design ; stratification

Abstract

Regression-based estimators are used for several surveys conducted by the Governments Division of the U.S. Census Bureau. One assumption of this style of estimator is that the auxiliary variable has a roughly linear relationship with the estimated variables. We propose a genetic algorithm to stratify the frame population with auxiliary data in such a way that the data fit a linear relationship in each stratum. To do this, we make the assumption that we know the maximum number of partitions for a piecewise linear fit. In particular, we consider the case of dividing an interval into at most three piecewise linear segments, with concepts that generalize naturally to any arbitrary maximum. We first explore two families of piecewise linear fits with different levels of perturbation. Finally, we apply this method to real Governments Division data.