Abstract

Daniell Toth and John L. Eltinge (2010) "Building Consistent Regression Trees from Complex Sample Data"

In the past several years the statistical literature has developed a wide range of methods for the construction of regression trees and other estimators based on the recursive partitioning of a sample. Many prospective applications involve data collected through a complex sample design. At present, however, relatively little is known regarding the properties of these methods under complex designs. This paper proposes a method for incorporating information about the complex sample design when building a regression tree using a recursive partitioning algorithm. Sufficient conditions are established which guarantee asymptotic design L2 consistency of these regression trees as an estimator for an arbitrary regression function. The proposed method is illustrated with Occupational Employment Statistics establishment survey data linked to Quarterly Census of Employment and Wage payroll data of the Bureau of Labor Statistics. Performance of the nonparametric estimator is investigated through a simulation study based on this example.