Degree Type

Dissertation

Date of Award

2003

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Jean-Didier Opsomer

Abstract

Nonresponse is a problem in survey sampling that occurs when part of the information that should be collected on the units selected to the sample is not observed. Unit nonresponse is the type of nonresponse where none of the characteristic of interest is measured for a particular set of units. A popular method to handle unit nonresponse is by increasing the sampling weights of the respondent units to compensate for the nonrespondents. In this class, two procedures are the weighting within cell estimator and the estimator that weighs the observations using estimated response probabilities, also known as propensity scores. In this dissertation, properties of these estimators are studied under a nonparametric response mechanism that allows for varying response probabilities. The response probabilities are assumed to be related to an auxiliary variable through a "smooth", but otherwise unspecified function. The weighting within cell estimator is proved to be consistent for the population mean. The impact of the number of cells on the asymptotic bias and variance of the estimator is also addressed. Empirical comparisons illustrate the superior performance of the estimator over an estimator that does not account for the nonresponse. The weighting with response probability estimator is implemented using a zero order local polynomial fit to estimate the response probabilities. Consistency of the resulting estimator for the population mean is established. Also, a replication estimator for the variance of the weighting with response probability estimator is constructed. Asymptotic properties of the variance estimator are derived.

DOI

https://doi.org/10.31274/rtd-180813-12130

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu

Copyright Owner

Damião Nóbrega da Silva

Language

en

Proquest ID

AAI3105107

File Format

application/pdf

File Size

139 pages

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