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The demand for reliable statistics has been growing over the past decades, because more and more political and economic decisions are based on statistics, e.g. regional planning, allocation of funds or business decisions. Therefore, it has become increasingly important to develop and to obtain precise regional indicators as well as disaggregated values in order to compare regions or specific groups. In general, surveys provide the information for these indicators only for larger areas like countries or administrative divisions. However, in practice, it is more interesting to obtain indicators for specific subdivisions like on NUTS 2 or NUTS 3 levels. The Nomenclature of Units for Territorial Statistics (NUTS) is a hierarchical system of the European Union used in statistics to refer to subdivisions of countries. In many cases, the sample information on such detailed levels is not available. Thus, there are projects such as the European Census, which have the goal to provide precise numbers on NUTS 3 or even community level. The European Census is conducted amongst others in Germany and Switzerland in 2011. Most of the participating countries use sample and register information in a combined form for the estimation process. The classical estimation methods of small areas or subgroups, such as the Horvitz-Thompson (HT) estimator or the generalized regression (GREG) estimator, suffer from small area-specific sample sizes which cause high variances of the estimates. The application of small area methods, for instance the empirical best linear unbiased predictor (EBLUP), reduces the variance of the estimates by including auxiliary information to increase the effective sample size. These estimation methods lead to higher accuracy of the variables of interest. Small area estimation is also used in the context of business data. For example during the estimation of the revenues of specific subgroups like on NACE 3 or NACE 4 levels, small sample sizes can occur. The Nomenclature statistique des activités économiques dans la Communauté européenne (NACE) is a system of the European Union which defines an industry standard classification. Besides small sample sizes, business data have further special characteristics. The main challenge is that business data have skewed distributions with a few large companies and many small businesses. For instance, in the automotive industry in Germany, there are many small suppliers but only few large original equipment manufacturers (OEM). Altogether, highly influential units and outliers can be observed in business statistics. These extreme values in connection with small sample sizes cause severe problems when standard small area models are applied. These models are generally based on the normality assumption, which does not hold in the case of outliers. One way to solve these peculiarities is to apply outlier robust small area methods. The availability of adequate covariates is important for the accuracy of the above described small area methods. However, in business data, the auxiliary variables are hardly available on population level. One of several reasons for that is the fact that in Germany a lot of enterprises are not reflected in business registers due to truncation limits. Furthermore, only listed enterprises or companies which trespass specific thresholds are obligated to publish their results. This limits the number of potential auxiliary variables for the estimation. Even though there are issues with available covariates, business data often include spatial dependencies which can be used to enhance small area methods. Next to spatial information based on geographic characteristics, group-specific similarities like related industries based on NACE codes can be used. For instance, enterprises from the same NACE 2 level, e.g. sector 47 retail trade, behave more similar than two companies from different NACE 2 levels, e.g. sector 05 mining of coal and sector 64 financial services. This spatial correlation can be incorporated by extending the general linear mixed model trough the integration of spatially correlated random effects. In business data, outliers as well as geographic or content-wise spatial dependencies between areas or domains are closely linked. The coincidence of these two factors and the resulting consequences have not been fully covered in the relevant literature. The only approach that combines robust small area methods with spatial dependencies is the M-quantile geographically weighted regression model. In the context of EBLUP-based small area models, the combination of robust and spatial methods has not been considered yet. Therefore, this thesis provides a theoretical approach to this scientific and practical problem and shows its relevance in an empirical study. ; In den letzten Jahren gab es einen steigenden Bedarf an disaggregierten Wirtschaftsdaten, da immer mehr Unternehmen und Institutionen ihre Entscheidungen auf Basis solcher Informationen treffen. Diese tiefgegliederten Daten können beispielsweise Umsätze von Unternehmen in einer speziellen Industrieklasse (NACE3- oder NACE4-Ebene) sein. Allerdings sind in der Realität Stichproben auf solch detailliertem Niveau selten verfügbar, was in der Regel kleine Stichprobenumfänge bewirkt. In solchen Fällen führen klassische Schätzverfahren oft zu schlechten Ergebnissen und Small Area Methoden müssen angewendet werden. Das Grundprinzip von diesen Verfahren besteht darin, dass die Schätzung durch Erweiterung der ursprünglich zu kleinen Datengruppe verbessert wird. Dies kann durch die Kombination der Erhebungsinformationen mit Hilfsvariablen, wie zum Beispiel Unternehmensdaten aus ähnlich strukturierten Industriezweigen, erreicht werden. Diese Methoden liefern unter strikten Annahmen über die Stichprobe und die Verteilung selbst bei kleinen Stichprobenumfängen deutlich bessere Schätzergebnisse als klassische Verfahren. Des Weiteren beinhalten einzelne Industrieklassen stark unterschiedlich ausgeprägte Werte. Ein Beispiel hierfür ist die Automobilindustrie, in der neben vielen kleineren Zulieferunternehmen auch einige große Hersteller in dieser Branche zu finden sind. Solche stark abweichenden Beobachtungen werden in der Statistik als Ausreißer bezeichnet. Bei Small Area Verfahren führt die Kombination von Ausreißern mit kleinen Stichprobenumfängen zu starken Problemen. Aus diesem Grund müssen Small Area Methoden gegenüber solch starken Beobachtungen robustifiziert werden. Derzeit gibt es in diesem Bereich zwei Ansätze: den robusten EBLUP und M-Quantile Modelle. Neben Ausreißern weisen aber Unternehmensdaten oft auch räumliche Muster auf, wie zum Beispiel geografische Nachbarschaftsstrukturen oder Branchenähnlichkeiten. Diese räumlichen Strukturen können ebenfalls benutzt werden, um die ursprünglich zu kleine Datengruppe zu erweitern. Die gleichzeitige Berücksichtigung von Ausreißern und räumlichen Mustern bei Schätzverfahren ist in der Wissenschaft jedoch noch nicht vollständig untersucht. Aus diesem Grund widmet sich die Arbeit dieser wissenschaftlich relevanten Problemstellung.

Composite spatial data on administrative area level are often presented by maps. The aim is to detect regional differences in the concentration of subpopulations, like elderly persons, ethnic minorities, low-educated persons, voters of a political party or persons with a certain disease. Thematic collections of such maps are presented in different atlases. The standard presentation is by Choropleth maps where each administrative unit is represented by a single value. These maps can be criticized under three aspects: the implicit assumption of a uniform distribution within the area, the instability of the resulting map with respect to a change of the reference area and the discontinuities of the maps at the borderlines of the reference areas which inhibit the detection of regional clusters. In order to address these problems we use a density approach in the construction of maps. This approach does not enforce a local uniform distribution. It does not depend on a specific choice of area reference system and there are no discontinuities in the displayed maps. A standard estimation procedure of densities are Kernel density estimates. However, these estimates need the geo-coordinates of the single units which are not at disposal as we have only access to the aggregates of some area system. To overcome this hurdle, we use a statistical simulation concept. This can be interpreted as a Simulated Expectation Maximisation (SEM) algorithm of Celeux et al (1996). We simulate observations from the current density estimates which are consistent with the aggregation information (S-step). Then we apply the Kernel density estimator to the simulated sample which gives the next density estimate (E-Step). This concept has been first applied for grid data with rectangular areas, see Groß et al (2017), for the display of ethnic minorities. In a second application we demonstrated the use of this approach for the so-called "change of support" (Bradley et al 2016) problem. Here Groß et al (2020) used the SEM algorithm to recalculate ...

The estimation of poverty and inequality indicators based on survey data is trivial as long as the variable of interest (e.g., income or consumption) is measured on a metric scale. However, estimation is not directly possible, using standard formulas, when the income variable is grouped due to confidentiality constraints or in order to decrease item nonresponse. We propose an iterative kernel density algorithm that generates metric pseudo samples from the grouped variable for the estimation of indicators. The corresponding standard errors are estimated by a non-parametric bootstrap that accounts for the additional uncertainty due to the grouping. The algorithm enables the use of survey weights and household equivalence scales. The proposed method is applied to the German Microcensus for estimating the regional distribution of poverty and inequality in Germany.

Consumer Price Indices (CPI) are used in many ways by the government, businesses, and society in general. They can affect interest rates, tax allowances, wages, state benefits, and many other payments. The CPI is a fixed (national) basket index, where a range of goods and services is priced each month, and the expenditure shares on items in the basket are used to weight the price information together. The starting point for a regional price index should be a regional basket of goods and services. In the current poster, we derive regional baskets from the UK Living Costs and Food Survey (LCF), taking the products (COICOP classification) with the largest proportion of expenditures. As the sample size is naturally much smaller for regions, the accuracy of the direct estimates on the basket will be reduced. In order to overcome this problem one possibility - discussed in the poster - is to pool multiple years of LCF data to increase the sample size. Another is to consider small area estimation approaches for the regional basket. Ideally, the small area estimates would be constrained to the overall expenditure total. Therefore, we assess some benchmarking approaches. Since the conceptual framework of CPI-calculation for the UK and Germany do not differ too much the presented methodology can also be adapted for the calculation of regional CPIs for Germany.

Abstract. Severe hailstorms result in substantial damage to buildings and vehicles, necessitating the quantification of associated risks. Here, we present a novel open-source hail damage model for buildings and cars based on single-polarization radar data and 250 000 geolocated hail damage reports in Switzerland from 2002 to 2021. To this end, we conduct a detailed evaluation of different radar-based hail intensity measures at 1 km resolution and find that the maximum expected severe hail size (MESHS) outperforms the other measures, despite a considerable false-alarm ratio. Asset-specific hail damage impact functions for buildings and cars are calibrated based on MESHS and incorporated into the open-source risk modelling platform CLIMADA. The model successfully estimates the correct order of magnitude for the number of damaged building in 91 %, their total cost in 77 %, the number of damaged vehicles in 74 %, and their total cost in 60 % of over 100 considered large hail events. We found considerable uncertainties in hail damage estimates, which are largely attributable to limitations of radar-based hail detection. Therefore, we explore the usage of crowdsourced hail reports and find substantially improved spatial representation of severe hail for individual events. By highlighting the potential and limitations of radar-based hail size estimates, particularly MESHS, and the utilization of an open-source risk modelling platform, this study represents a significant step towards addressing the gap in risk quantification associated with severe hail events in Switzerland.

The R package emdi enables the estimation of regionally disaggregated indicators using small area estimation methods and includes tools for processing, assessing, and presenting the results. The mean of the target variable, the quantiles of its distribution, the headcount ratio, the poverty gap, the Gini coefficient, the quintile share ratio, and customized indicators are estimated using direct and model-based estimation with the empirical best predictor (Molina and Rao 2010). The user is assisted by automatic estimation of datadriven transformation parameters. Parametric and semi-parametric, wild bootstrap for mean squared error estimation are implemented with the latter offering protection against possible misspecification of the error distribution. Tools for (a) customized parallel computing, (b) model diagnostic analyses, (c) creating high quality maps and (d) exporting the results to Excel and OpenDocument Spreadsheets are included. The functionality of the package is illustrated with example data sets for estimating the Gini coefficient and median income for districts in Austria.