Warnholz, Sebastian
[Verfasser:in]
;
sebastian.warnholz@fu-berlin.de
[Mitwirkende:r];
Timo Schmid
[Mitwirkende:r];
Nikos Tzavidis
[Mitwirkende:r]
Small Area Estimation Using Robust Extensions to Area Level Models ; Theory, Implementation and Simulation Studies ; Small-Area-Statistik mit robusten Erweiterungen für Area-Level-Modelle ; Theorie, Implementierung und Simulationsstudien
Titel:
Small Area Estimation Using Robust Extensions to Area Level Models ; Theory, Implementation and Simulation Studies ; Small-Area-Statistik mit robusten Erweiterungen für Area-Level-Modelle ; Theorie, Implementierung und Simulationsstudien
Beteiligte:
Warnholz, Sebastian
[Verfasser:in]
Erschienen:
Freie Universität Berlin: Refubium (FU Berlin), 2016
Anmerkungen:
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Beschreibung:
The demand for reliable small area statistics from sample surveys has grown substantially over the past decades due to their growing use in public and private sectors. The field of Small Area Estimation aims at producing such statistics. In this Thesis I consider several spatial and temporal extensions to the Fay-Herriot (FH) Model to improve the mean squared prediction error (MSPE) of predictions for small domains. Such predictions can be influenced by single observations in the data; hence the estimation of the model parameters and predictions is based on the estimation methodology around robust empirical best linear unbiased predictions (REBLUPs). With regard to robust area level models four such models are under consideration: the FH model, a spatial extension, a temporal extension and a spatio-temporal model. These methods are extended to obtain (i) an area level robust EBLUP (REBLUP); (ii) an area level spatial REBLUP (SREBLUP); (iii) a temporal REBLUP (TREBLUP); and (iv) a spatio-temporal REBLUP (STREBLUP). I present these methods in a comprehensive framework of robust area level models. For the estimation of the MSPE a parametric bootstrap method is adapted as well as a analytical solution based on a pseudolinear representation of the predictors. In this context also a bias correction based on a limited translation estimator is adapted to account for a potential bias associated to robust methods. In addition to the development of these robust methods their implementation in the R-package saeRobust is investigated. The package provides an initial version for the application of the developed methodology. In this regard some numerical stability tests are performed and also basic features like diagnostic plots for model residuals are reviewed. Also an outcome of this Thesis is the package saeSim which provides a framework for simulation studies within the R-language. It aims at simplifying the configuration of such studies by providing tools for data generation, sampling, and a link to the parallel computing ...