Statistica Sinica 23 (2013), 189-211

doi:http://dx.doi.org/10.5705/ss.2011.272

NONPARAMETRIC ENDOGENOUS

POST-STRATIFICATION ESTIMATION

Mark Dahlke$^1$, F. Jay Breidt$^1$, Jean D. Opsomer$^1$ and Ingrid Van Keilegom$^2$

$^1$Colorado State University and $^2$Université catholique de Louvain

Abstract: Post-stratification is used to improve the precision of survey estimators when categorical auxiliary information is available from external sources. In natural resource surveys, such information may be obtained from remote sensing data classified into categories and displayed as maps. These maps may be based on classification models fitted to the sample data. Such ``endogenous post-stratification'' violates the standard assumptions that observations are classified without error into post-strata, and post-stratum population counts are known. Properties of the endogenous post-stratification estimator (EPSE) are derived for the case of sample-fitted nonparametric models, with particular emphasis on monotone regression models. Asymptotic properties of the nonparametric EPSE are investigated under a superpopulation model framework. Simulation experiments illustrate the practical effects of first fitting a nonparametric model to survey data before post-stratifying.

Key words and phrases: Monotone regression, smoothing, survey estimation.