Nonparametric Density Estimation in Survey Sampling

Abstract

Nonparametric methods for estimating probability densities are popular because they provide flexible tools for exploratory analysis, model checking, and inference when little is known about the underlying distributional form. In the context of sample surveys where data arise from complex designs involving stratification, clustering, and unequal inclusion probabilities, naive application of standard nonparametric estimators can, however, produce biased and inconsistent results. This paper reviews foundations of nonparametric density estimation and use of kernel and local polynomial methods and discusses their adaptation to design-based and model-based survey frameworks. Practical implementation issues involving bandwidth selection, boundary correction, and computational considerations are made. Throughout, emphasis is placed on methods that respect survey design information, and on trade-offs between design-based validity and model-based efficiency. The paper concludes with recommendations for practice and directions for future research.