Model-based Methods for Robust Finite Population Inference in the Presence of External Information.

Abstract

This dissertation develops new model-based approaches for analysis of sample survey data. The main focus of the thesis is to incorporate information available from external sources to improve estimation and inference for finite population quantities. If such information is utilized properly, it can improve point estimates and inferences. The dissertation addresses two general scenarios: survey data from unequal probability designs and surveys with nonresponse.

The first part of the dissertation studies robust Bayesian methods for finite population inference in probability proportional to size (PPS) sampling. First, I study Bayesian inference of the population total from a heteroscedastic probability proportional to size sample. I first propose a Bayesian penalized spline model that models non-constant error variance. When the sizes of nonsampled units are unavailable for analysis, I combine the proposed spline model with a constrained Bayesian bootstrap model adjusted for PPS selection.

The proposed imputation methodology is next extended and generalized to provide a flexible framework for recovering the missing design information for model-based inference using Bayesian nonparametric mixture modeling with Dirichlet process priors. When the design variables that govern the selection mechanism are missing, the sample design becomes informative and predictions need to be adjusted for the effect of selection. Imputations based on Bayesian nonparametric methods under different choices of priors are compared for various population structures and sample sizes. Strengths and limitations of the proposed methods are evaluated empirically via simulations.

The final part of the dissertation focuses on maximum likelihood estimation for the population mean for a survey experiencing unit nonresponse, i.e., when a sampled unit does not respond to the entire survey. I consider situations where post-stratification information is externally available for the population. Without external information, unit nonresponse, would lead to missing-data mechanisms that are missing not at random (MNAR), which generally require a model for the missing-data mechanism. Approaches to weakening the MAR assumption by inclusion of external information are developed for situations where the data are MNAR in the classical sense defined by Rubin (1976), but post-stratification information is externally available.