Model-based methods for small area estimation
Typ dokumentu
habilitation thesishabilitační práce
Autor
Hobza, Tomáš
Metadata
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This thesis summarizes main results of the author obtained in the field called “small area
estimation” (SAE). SAE is a branch of mathematical statistics which deals with the problem
of estimating population parameters in subsets (called areas or domains) of a population where
the sample sizes are not large enough to provide reliable direct estimates. For this purpose, SAE
introduces statistical models that “borrow strength” from related small areas, data from external
administrative sources or data from different time periods. An overview of basic principles,
models and problems encountered in SAE is given in the first part of the thesis.
The contribution of the author in the form of published papers is presented in the second part
of the thesis and consists of several models proposed for estimation of small area parameters.
These models are based on linear mixed and generalized linear mixed models. Namely, there are
proposed and studied several modifications of Fay-Herriot and nested error regression models
and there are considered logistic mixed models for binary data. For all the assumed models
the following problems are treated. Formulas and algorithms for estimation of the unknown
parameters of the models are derived. Model-based empirical best predictors of parameters of
small areas are studied. Special attention is paid to estimation of the mean squared error of
the predictors since such a measure of accuracy is needed in practical applications. For all the
models analytic approximation or bootstrap estimates of the mean squared errors are given.
An important part of developing a new model is to design and carry out simulation experi ments studying small sample size behaviour of the new methods and comparing them with the
existing ones if there are any available. It means that development of non-trivial software tools
is an integral part of the presented works since the standard statistical packages cannot be used
for the studied models and moreover Monte Carlo approximation methods must often be used.
Further, to show applicability and benefits of the proposed methods in practice, a real data
application are performed in all the papers.
In addition, several results of the author which are connected with robust estimation and
outlier detection in generalized linear models and which can be applied to small area estimation
problems are presented.
Kolekce
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