Estimating Distribution Functions from Survey Data Using Nonparametric Regression

Survey sampling often supplies information about a study variable only for sampled elements. However, auxiliary information is often available for the entire population. The relationship of the auxiliary information with the study variable across the sample allows inferences about the nonsampled portion of the population. Thus, auxiliary information can be used to improve upon survey estimation. In particular, finite population distribution function estimation can be improved. Existing parametric estimators incorporate auxiliary information by assuming it to have a linear relationship with the study variable, which is often unreasonable or unverifiable in survey sampling. A model-assisted nonparametric estimator based on local polynomial regression is introduced which removes these parametric restrictions by working under a more generic context. A Monte Carlo comparison of this estimator with parametric estimators demonstrates its superior efficiency for estimation of the distribution function and quantiles in most cases in which the parametric methods misspecify the relationship between the auxiliary and study variables. Finally, a semiparametric estimator is introduced which allows for the incorporation of parametric fixed effects, including categorical variables. When applied to a population of Northeastern lakes, this estimator is more efficient on average than a more conventional estimator that does not incorporate any auxiliary information.