Penalized spline nonparametric regression methods for survey samples with potentially unequal probabilities of inclusion

For survey samples with unequal probabilities of inclusion, the Horvitz-Thompson (HT) estimator and its extensions are often used to give unbiased or design-consistent estimation of finite population quantities. From the modeling point of view, most of the design-based estimators coincide with model-based estimators for some parametric models. For example, the HT estimator corresponds to a no-intercept linear regression model regressing y_i on π _i with error variances proportional to $p2i$. These design-based estimators can be inefficient when the underlying parametric model assumptions are not met.; In this thesis, I discuss alternative estimation methods using nonparametric regression models in one-stage and two-stage samples. I also study three variance estimation methods for those model-based estimators, namely, the empirical Bayes, the jackknife and balanced repeated replicate (BRR) variance estimation methods.; Chapter I gives an overview of existing design-based and model-based theory and methods for estimation of finite population quantities.; Chapter II presents penalized spline (p-spline) model-based estimation for finite population totals from probability-proportional-to-size (PPS) samples. The mean of outcome variable y_i is modeled as a smoothly-varying function of the inclusion probability π _i. The flexible model yields improvements over HT estimator and linear model-assisted estimators.; In Chapter III, empirical Bayes, jackknife and BRR variance estimators are developed for the above-proposed estimators. The corresponding inference methods are compared with those based on HT, combined with five alternative variance estimators. Theory is provided to justify the jackknife method in the context of p-spline model-based approach.; In Chapter IV, estimators based on p-spline model with random cluster effects are proposed for estimating a finite population mean in two-stage sampling designs. This method allows for modeling the clustering effects while maintaining a nonparametric mean structure. The corresponding estimator is more efficient than inverse probability weighted estimators and linear model-assisted estimators. The empirical Bayes posterior variance, the jackknife and BRR variance estimators are found to yield good inferences for the population mean.; In Chapter V, other possible applications of nonparametric modeling in survey research are discussed.; Throughout this thesis, simulated and real datasets are used to make comparisons among the proposed and existing alternative methods.