Models and methods for three problems in survey statistics: Subsampling callbacks to improve survey efficiency; model-based alternatives to weight trimming; and methods for combining information from a census, a coverage measurement survey, and demographic analysis.

Abstract

In this dissertation I provide new theory and methodology to address three important problems in sample survey statistics: the question of whether and how to randomly subsample difficult-to-reach non-respondents to improve survey efficiency, methods for trimming or smoothing sampling weights to reduce variance in statistical estimators, and methods for combining information from follow surveys and demographic analysis to improve estimates of the undercounted population in the US Census. I first consider randomly subsampling an alpha proportion of the non-contacted units in the original sample from the <italic> m</italic>th callback forward as an extension on of Neyman or optimal allocation, and determine the ratio of the total data collection costs under the subsampling versus the full callback strategy as a function of the mean, cost, and probability-of-interview structures. Regarding weight trimming, I consider an extension of the standard weight-trimming approach by developing a Bayesian variable selection model to obtain a stratum-collapsing estimator sensitive to bias-variance tradeoffs. An alternative approach to weight trimming uses random-effects models to borrow information across inclusion strata; I also propose a non-parametric random-effects model that is robust against mean structure misspecification. These estimators perform well when compared with alternative stratum-collapsing and random-effect estimators. For the undercount problem, I review a number of models that have been proposed to accomplish a synthesis of information from the Census, coverage measurement surveys and demographic information when the demographic information is in the form of sex ratios stratified by age and race. I propose some general principles for aiding the choice among alternative models. I then pick a particular model based on these principles, and embed it within a more comprehensive Bayesian model for counts in poststrata of the population that (a) provides a principled solution to the existence of negative estimated counts in some subpopulations; (b) allows a test of whether negative cell counts are due to sampling variability or more egregious problems such as bias in Census or coverage measurement survey counts; (c) provides for smoothing of estimates across poststrata; and (d) provides estimates of precision that can incorporate uncertainty in the estimates from demographic analysis and other sources.