Year

2011

Degree Name

Doctor of Philosophy

Department

School of Mathematics and Applied Statistics

Abstract

Many different Small Area Estimation (SAE) methods have been proposed to overcome the challenge of finding reliable estimates for small domains. Often, the required data for various research purposes are available at different levels of aggregation. Based on the available data, individual-level or aggregated-level models are used in SAE. If unit-level data are available, SAE is usually based on models formulated at the unit level but they are ultimately used to produce estimates at the area level. However, parameter estimates obtained from individual and aggregated level analysis may be different in practice. Individual-level analysis usually results in small area estimates with smaller variances. However, if the unit-level working model is misspecified by exclusion of important auxiliary variables, parameter estimates obtained from the individual and aggregated level analysis will have different expectations.

This thesis investigates the circumstances when using an area-level model may be more effective. This may happen due to some substantial contextual or area-level effects in the covariates which may be misspecified in an individual-level model. Ignoring these contextual effects leads to biased estimates. In particular, if an existing contextual variable is ignored, the parameter estimates calculated from an individual-level analysis will be biased, whereas an aggregated-level analysis can lead to small area estimates with less bias. Even if contextual variables are included in unit-level modeling, there may be an increase in the variance of parameter estimates due to increased number of variables in the working model. In this thesis, synthetic estimators and Empirical Best Linear Unbiased Predictors (EBLUPs) are evaluated in SAE based on different levels of linear mixed models. Using a numerical simulation study, the key role of contextual effects is examined for models used in SAE.

FoR codes (2008)

0199 OTHER MATHEMATICAL SCIENCES

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Unless otherwise indicated, the views expressed in this thesis are those of the author and do not necessarily represent the views of the University of Wollongong.