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Freie Universität Berlin

1. Baldermann, Claudia. Robust Small Area Estimation under Spatial Non-Stationarity for Unit-Level Models.

Degree: PhD, FB Wirtschaftswissenschaft, 2017, Freie Universität Berlin

The demand for reliable small area statistics has been growing in public and private organizations. Sample surveys are designed to produce reliable estimates for quantities of interest on higher geographic levels, but can have very small or even zero sample sizes for lower geographic levels. Direct estimates, which only rely on area-specific information, are usually unbiased but can produce results with high variability in the case of small sample sizes. Small area estimation (SAE) techniques have been developed to gain reliability compared to direct estimates by borrowing strength from additional information. One well known SAE method is the empirical best linear unbiased predictor (EBLUP) of the small area mean that incorporates auxiliary variables using the linear mixed model approach. In addition, spatial information can be used to borrow strength over space. One approach to account for geographical information is to extend the linear mixed model and allow for spatially correlated random area effects (cf. Pratesi and Salvati, 2008, SEBLUP). An alternative is to include the spatial information by non-parametric mixed models (cf. Opsomer et al., 2008, NPEBLUP). Another option is the geographic weighted regression where the model coefficients vary across the study area (cf. Chandra et al., 2012, GWEBLUP). Under the assumption of normally distributed error terms, these approaches are useful for estimating small area means efficiently. The normality assumption can be violated in the presence of outliers and, hence, it can be beneficial to reduce the influence of outliers and use robust methods for SAE (cf. Sinha and Rao, 2009). This thesis extends the current literature by providing robust extensions for the GWEBLUP of the area mean. In particular, a robust projective and a robust predictive version of the GWEBLUP is proposed. In addition, two analytic MSE estimates are developed based on the pseudo-linearization approach of Chambers et al. (2011) and under the full linearization approach of Chambers et al. (2014). The proposed methods have been implemented for the R-language (R Core Team, 2016) in the package saeRGW. The performance of the proposed methods is assessed in model and design-based simulation studies. The model-based simulation indicates that in the presence of spatial non-stationarity and outliers, applying the proposed robust methods can lead to efficiency gains compared to the non-robust GWEBLUP of the small area mean. In addition, the proposed MSE estimators show good properties in terms of bias and stability in the investigated scenarios. The design-based simulation also indicates that in case of the Berlin real estate database it can be beneficial to combine the GWEBLUP with robust protection for estimating small area means of the quoted net rent.

Small-Area-Verfahren gewinnen zunehmend an Bedeutung in der amtlichen Statistik und privaten Institutionen. Bevölkerungsstichproben liefern in der Regel verlässliche Schätzungen für aggregierte Populationsgrößen,…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Baldermann, C. (2017). Robust Small Area Estimation under Spatial Non-Stationarity for Unit-Level Models. (Doctoral Dissertation). Freie Universität Berlin. Retrieved from http://edocs.fu-berlin.de/diss/receive/FUDISS_thesis_000000105851

Chicago Manual of Style (16th Edition):

Baldermann, Claudia. “Robust Small Area Estimation under Spatial Non-Stationarity for Unit-Level Models.” 2017. Doctoral Dissertation, Freie Universität Berlin. Accessed December 15, 2017. http://edocs.fu-berlin.de/diss/receive/FUDISS_thesis_000000105851.

MLA Handbook (7th Edition):

Baldermann, Claudia. “Robust Small Area Estimation under Spatial Non-Stationarity for Unit-Level Models.” 2017. Web. 15 Dec 2017.

Vancouver:

Baldermann C. Robust Small Area Estimation under Spatial Non-Stationarity for Unit-Level Models. [Internet] [Doctoral dissertation]. Freie Universität Berlin; 2017. [cited 2017 Dec 15]. Available from: http://edocs.fu-berlin.de/diss/receive/FUDISS_thesis_000000105851.

Council of Science Editors:

Baldermann C. Robust Small Area Estimation under Spatial Non-Stationarity for Unit-Level Models. [Doctoral Dissertation]. Freie Universität Berlin; 2017. Available from: http://edocs.fu-berlin.de/diss/receive/FUDISS_thesis_000000105851

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