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Spatially disaggregated income indicators are typically estimated by using model-based methods that assume access to auxiliary information from population micro-data. In many countries like Germany and the UK population micro-data are not publicly available. In this work we propose small area methodology when only aggregate population-level auxiliary information is available. We use data-driven transformations of the response to satisfy the parametric assumptions of the used models. In the absence of population micro-data, appropriate bias-corrections for small area prediction are needed. Under the approach we propose in this paper, aggregate statistics (means and covariances) and kernel density estimation are used to resolve the issue of not having access to population micro-data. We further explore the estimation of the mean squared error using the parametric bootstrap. Extensive model-based and design-based simulations are used to compare the proposed method to alternative methods. Finally, the proposed methodology is applied to the 2011 Socio-Economic Panel and aggregate census information from the same year to estimate the average income for 96 regional planning regions in Germany.

Continuously emerging additive manufacturing technologies, especially developments within the last decade, offer new opportunities for producing metallic parts. The project 2ARMY addresses the growing needs regarding the on-demand production of spare parts and repairing worn metallic components. The maintenance units can use mobile deployable workshops for additive manufacturing and significantly improve the availability of critically important weapon systems and equipment on the battlefield. The possibility of producing the old and eventually unavailable parts in sufficient quality and maintaining existing worn parts is expected to have a positive economic impact on the lifetime of related systems and their short-time availability. It can be especially relevant for military use. Three vital system components of such a mobile and partially autonomous robotic cell for wire and arc additive manufacturing and repair of metallic parts were investigated during the project. Optical 3D acquisition of the part's actual shape and computation of the difference to the expected part's geometry is desirable for process automation. An appropriate 3D-scanning system has been found and integrated with available robotic welding cell. Algorithms were developed for automatically detecting the damaged regions on the part and for path generation according to the suitable manufacturing strategy. Furthermore, the current challenges regarding the quality assurance of additively manufactured parts were addressed. A digital signal acquisition chain was developed to monitor dynamic GMAW process variants. The designed database allows more in-depth analysis of the manufacturing process and optimisation of the non-destructive testing methods. A damaged part has been repaired, and a spare part has been produced to illustrate the capability of the methods, algorithms and system components developed during the project 2ARMY., The projects 2ARMY (Proj. Nr: 873477) and 2ARMY II (Proj. Nr: 895157) have been funded by the Austrian defense research programme FORTE of the Federal Ministry of Finance (BMF)., {"references":["C. R. Cunningham, J. M. Flynn, A. Shokrani, V. Dhokia und S. T. Newman, \"Invited review article: Strategies and processes for high quality wire arc additive manufacturing,\" Additive Manufacturing, Jg. 22, S. 672–686, 1. Aug. 2018, ISSN: 2214-8604. DOI: 10.1016/j.addma.2018.06.020","Y. K. Bandari, T. O. H. Charrett, F. Michel, J. Ding et al., \"Compensation strategies for robotic motion errors for additive manufacturing (AM),\" University of Texas, 10. Aug. 2016. [Online]. Adresse: https://dspace.lib.cranfield.ac.uk/handle/1826/12561","Additive Fertigung - Prozessanforderungen Und Qualifizierung - Teil 1: Materialauftrag mit gerichteter Energieeinbringung unter Verwendung von draht und Laser in der Luft- Und Raumfahrt, DIN 17024-1:2020-02, Berlin, Sep. 2021. DOI: 10.31030/3130636","D. Nikolaev und R. Sommerhuber, \"GMAW & WAAM Process monitoring using XARION Eta300 Ultra laser microphone\". Zenodo, 2. März 2020. doi: 10.5281/ZENODO.7768265"]}

This paper promotes the use of random forests as versatile tools for estimating spatially disaggregated indicators in the presence of small area-specific sample sizes. Small area estimators are predominantly conceptualized within the regression-setting and rely on linear mixed models to account for the hierarchical structure of the survey data. In contrast, machine learning methods offer non-linear and non-parametric alternatives, combining excellent predictive performance and a reduced risk of model-misspecification. Mixed effects random forests combine advantages of regression forests with the ability to model hierarchical dependencies. This paper provides a coherent framework based on mixed effects random forests for estimating small area averages and proposes a non-parametric bootstrap estimator for assessing the uncertainty of the estimates. We illustrate advantages of our proposed methodology using Mexican income-data from the state Nuevo Le\'on. Finally, the methodology is evaluated in model-based and design-based simulations comparing the proposed methodology to traditional regression-based approaches for estimating small area averages., Comment: Working Paper

Reliable estimators of the spatial distribution of socio-economic indicators are essential for evidence-based policy-making. As sample sizes are small for highly disaggregated domains, the accuracy of the direct estimates is reduced. To overcome this problem small area estimation approaches are promising. In this work we propose a small area methodology using machine learning methods. The semi-parametric framework of mixed effects random forest combines the advantages of random forests (robustness against outliers and implicit model-selection) with the ability to model hierarchical dependencies. Existing random forest-based methods require access to auxiliary information on population-level. We present a methodology that deals with the lack of population micro-data. Our strategy adaptively incorporates aggregated auxiliary information through calibration-weights - based on empirical likelihood - for the estimation of area-level means. In addition to our point estimator, we provide a non-parametric bootstrap estimator measuring its uncertainty. The performance of the proposed point estimator and its uncertainty measure is studied in model-based simulations. Finally, the proposed methodology is applied to the $2011$ Socio-Economic Panel and aggregate census information from the same year to estimate the average opportunity cost of care work for $96$ regional planning regions in Germany., Comment: Working Paper

Like many other countries, the United Kingdom (UK) produces a national consumer price index (CPI) to measure inflation. Presently, CPI measures are not produced for regions within the UK. It is believed that, using only available data sources, a regional CPI would not be precise or reliable enough as an official statistic, primarily because the regional partitioning of the data makes sample sizes too small. We investigate this claim by producing experimental regional CPIs using publicly available price data, and deriving expenditure weights from the Living Costs and Food survey. We detail the methods and challenges of developing a regional CPI and evaluate its reliability. We then assess whether model-based methods such as smoothing and small area estimation significantly improve the measures. We find that a regional CPI can be produced with available data sources, however it appears to be excessively volatile over time, mainly due to the weights. Smoothing and small area estimation improve the reliability of the regional CPI series to some extent but they remain too volatile for regional policy use. This research provides a valuable framework for the development of a more viable regional CPI measure for the UK in the future.

Fragestellung: Kompressionssonografie wurde zur nicht-invasiven Messung der Kompartimentelastizität und als mögliches Diagnosewerkzeug für das akute oder chronische Kompartmentsyndrom eingeführt und bereits in Studien mit menschlichen Leichen- und Tiermodellen angewendet. Bisher [zum vollständigen Text gelangen Sie über die oben angegebene URL]

Censuses are fundamental building blocks of most modern-day societies, yet collected every 10 years at best. We propose an extension of the widely popular census updating technique structure-preserving estimation by incorporating auxiliary information in order to take ongoing subnational population shifts into account. We apply our method by incorporating satellite imagery as additional source to derive annual small-area updates of multidimensional poverty indicators from 2013 to 2020 for a population at risk: female-headed households in Senegal. We evaluate the performance of our proposal using data from two different census periods.

The Greenland Ice Sheet (GrIS) has experienced increasing ice loss in the past decades and the trend is expected to continue due to climate change. However, large uncertainties about the magnitude of Greenland’s future ice loss remain. One process that contributes to this uncertainty are transient ice accelerations, so-called ice speed-up events, caused by a short-term increase in rain-/meltwater, which descends to the glacier bed and can enhance basal sliding. Here, we investigate this phenomenon focusing on two main objectives. First, we present an analysis of local conditions on the Russell glacier in Southwest Greenland, which confirms the importance of meltwater variability for ice speed-up events. We find the strongest influence in early summer with correlations between surface melt and ice velocities above 0.8 in May and identify a typical lag of zero to one day between meltwater peaks and their ice velocity responses. Contrastingly, we find rainfall to have a minor influence with only 4 out of 51 ice speed-up events, where daily increases in water input on the glacier are dominated by rainfall. Secondly, we study the atmospheric drivers of ice speed-up events using a Self-Organizing Maps (SOM) classification of synoptic weather situations over Greenland. Two main patterns that induce most ice speed-up events emerge: The first pattern is characterized by southerly advection of warm and moist air that increases local surface melting by enhanced downward longwave radiation and high sensible heat flux. The second one is a large-scale anticyclone that induces GrIS surface melting through strong downward shortwave radiation and descending air that warm adiabatically. Our study provides new insights into atmospheric drivers of short-term ice accelerations and contributes towards an effort to constrain the impact of ice speed-up events on GrIS mass loss under a changing climate, which can be achieved when more high-resolution ice velocity data is available.

The transformation of area aggregates between non-hierarchical area systems (administrative areas) is a standard problem of official statistics. For this problem, we present a proposal which is based on kernel density estimates. The approach applies a modification of a stochastic expectation maximization algorithm, which was proposed in literature for the transformation of totals on rectangular areas to kernel density estimates. As a by-product of the routine, one obtains simulated geo-coordinates for each unit. With the help of these geo-coordinates, it is possible to calculate case numbers for any area system of interest. The proposed method is evaluated in a design-based simulation based on a close-to-reality, simulated data set with known exact geo-coordinates. In the empirical part, the method is applied to student resident figures from Berlin. These are known only at the level of ZIP codes but they are needed for smaller administrative planning districts. Results for a) student concentration areas and b) temporal changes in the student residential areas between 2005 and 2015 are presented and discussed.

Background Significant inequalities in caries distribution among children in Germany have been reported, but small‐scale areas remain understudied. Aim To examine spatio‐temporal trends in children's dental caries at the small‐area level in Berlin‐Mitte. Design Routinely collected data from Berlin's annual Health Examination Surveys were used, which also include information on age, sex, country of origin, and residential area. The study population consists of 14,866 children aged 5 to 7 between 2006 and 2014 in the district of Berlin‐Mitte. Outcome variables are the dmft (decayed, missing, and filled teeth), the presence of any caries experience, untreated caries, and caries risk. The outcomes are summarized descriptively and graphically presented for 10 quarters and 41 communities within Berlin‐Mitte. Results Relevant gaps in children's dental caries were discovered between the quarters of Mitte. Three quarters in the northeast part of Mitte have consistently indicated the lowest oral health status in all four outcomes, and children having high caries risk have been increasingly concentrating in this area over time. Despite the continuous improvements in the southern part, the averages in total of Mitte for all outcomes have risen. Conclusion Our findings confirm the spatiotemporally mounting disparities in children's oral health between the quarters in Berlin‐Mitte and that particular quarters need urgent attention. The small‐area approach made it easier and more effective to reveal the spatial distribution of children's dental caries at the local level. The small‐area analysis should be strongly encouraged in future caries research to narrow the inequalities in children's oral health.

M-quantile regression is a general form of quantile-like regression which usually utilises the Huber influence function and corresponding tuning constant. Estimation requires a nuisance scale parameter to ensure the M-quantile estimates are scale invariant, with several scale estimators having previously been proposed. In this paper we assess these scale estimators and evaluate their suitability, as well as proposing a new scale estimator based on the method of moments. Further, we present two approaches for estimating data-driven tuning constant selection for M-quantile regression. The tuning constants are obtained by i) minimising the estimated asymptotic variance of the regression parameters and ii) utilising an inverse M-quantile function to reduce the effect of outlying observations. We investigate whether data-driven tuning constants, as opposed to the usual fixed constant, for instance, at c=1.345, can improve the efficiency of the estimators of M-quantile regression parameters. The performance of the data-driven tuning constant is investigated in different scenarios using model-based simulations. Finally, we illustrate the proposed methods using a European Union Statistics on Income and Living Conditions data set., Comment: 30 pages, 6 figures

There is a huge interest in deriving and comparing socio-economic indicators across societal groups and domains. The indicators are usually derived from population surveys like the German Socio-Economic Panel (SOEP) by direct estimation. Small sample sizes in the domains can limit the precision of these estimates. For example, while SOEP may be a suitable database for determining mean income in Germany, it is unclear whether this also applies to smaller domains (for example, women in Berlin). Here we show SOEP-based applications of Stata's fayherriot package (Halbmeier et al., 2019). This package implements the Fay-Herriot model (Fay and Herriot, 1979), a small-area estimation technique designed to improve the precision of domain-level direct estimates using domain-level covariates from auxiliary datasets.

More than 25 years after German reunification, key economic indicators for households living in eastern German regions are still below the western German levels. This particularly holds for private net wealth, which reaches only about 40% of the western German level. However, a more granular regional perspective may reveal a more diverse picture. Therefore, this study is designed to develop regional wealth indicators for the 16 federal states and for the 96 regional planning regions (Raumordnungsregionen) in Germany based on the second wave of the Panel on Household Finances (PHF) conducted by the Deutsche Bundesbank in 2014. These estimates are derived by means of a modified Fay-Herriot approach (Fay and Herriot, 1979) dealing with a) the skewness of the wealth distribution using a transformation, b) unit and item non-response, especially the multiple imputation used, and c) inconsistencies of the regional estimates with the national direct estimate. The results show that private wealth in all eastern German regions still remains far below the national average. However, the wealthiest planning regions in the east report higher private wealth figures than the western German regions with the lowest private wealth estimates. Although the paper is particularly focused on Germany, the approach proposed is applicable to surveys with a similar data structure.

The transformation of area aggregates between non-hierarchical area systems is a standard problem of official statistics. We introduce a new method which is based on kernel density estimates. It is a modification of the SEM algorithm proposed by Gross et al. (2016), which was used for the transformation of totals on rectangular areas to kernel densities estimates. As a by-product of the routine one obtains simulated geo-coordinates for each unit. With the help of these geo-coordinates it is possible to calculate case numbers for a new area system. The method is applied to student resident figures from Berlin. These are known only at the level of ZIP codes but they are needed for administrative planning districts. Our method is evaluated on a similar, simulated data set with known exact geo-coordinates. In the empirical part results for changes in the student residential areas between 2005 and 2015 are presented. It is demonstrated that the transformation via kernel density estimates offers additional useful features to display concentration areas.

Map-based regional analysis is interested to detect areas with a large concentration of certain populations. Here kernel density estimates (KDE) offer advantages over classical choropleth maps. However, kernel density estimation needs exact geo-coordinates. In a recent paper Groß et al. (2017) have proposed a measurement error model which uses local aggregates for kernel density estimation. Their algorithm simulates "exact" geo-coordinates which reflect the information on the aggregates. In this article we suggest two extensions of this approach. First, we consider boundary constraints, which are usually ignored in the KDE framework. This concerns not only the outer limits of a municipality but also unsettled regions within a city like parks, lakes and industrial areas. Without a boundary correction standard KDEs underestimate the density in the vicinity of boundaries. Here we propose a modification of the original algorithm which uses rescaled kernel functions. Regional maps often display local percentages, for example, voters for a special party among all voters in each voting district. Here we derive a smooth representation of percentages which is based on the ratio of two densities. Again, the original algorithm is modified to cope with the estimation of a ratio of two densities. Our empirical examples refer to voting results from Berlin. It is shown that the proposed methodology reveals a lot of regional insight which is not produced by standard choropleth maps.

In the last decades policy decisions are often based on statistical measures. The more detailed this information is, the better is the basis for targeting policies and evaluating policy programs. For instance, the United Nations suggest more disaggregation of statistical indicators for monitoring their Sustainable Development Goals and also the number of National Statistical Institutes (NSIs) that notice the need of more disaggregated statistics is increasing. Dimensions for disaggregation can be characteristics of the individuals or households like sex, age or ethnicity, economic activity or spatial dimensions like metropolitan areas or districts. Primary data sources for variables that are used to estimate statistical indicators are national household surveys. However, sample sizes are usually small or even zero at disaggregated levels. Therefore, direct estimators based only on survey data can be unreliable or not available for small domains. While the option of more specific surveys is costly, model-based methodologies for dealing with small sample sizes can help to obtain reliable estimates for small domains. The so-called Small Area Estimation (SAE) methods [1,2] link survey data that is only available for a proportion of households with administrative or census data available for all households in the area of interest. Even though a wide range of SAE methods is proposed by academic researchers, these are, so far, applied only by a small number of NSIs or other practitioners like the World Bank. This gap between theoretical possibilities and practical application can have several reasons. One reason can be the lack of suitable statistical software. The free software environment R helps to counteract this issue since researchers can make their codes available to the public via packages. Thus, new methods can reach the practitioner faster than with non-free software. The next two sections summarize which packages are already available and what could be improved in the future.

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-calculationfor the UK and Germany do not differ too much the presented methodology can also be adapted for the calculation of regional CPIs for Germany.

Among a variety of small area estimation methods, one popular approach for the estimation of linear and non-linear indicators is the empirical best predictor. However, parameter estimation using standard maximum likelihood methods is not possible, when the dependent variable of the underlying nested error regression model, is censored to specific intervals. This is often the case for income variables. Therefore, this work proposes an estimation method, which enables the estimation of the regression parameters of the nested error regression model using interval censored data. The introduced method is based on the stochastic expectation maximization algorithm. Since the stochastic expectation maximization method relies on the Gaussian assumptions of the error terms, transformations are incorporated into the algorithm to handle departures from normality. The estimation of the mean squared error of the empirical best predictors is facilitated by a parametric bootstrap which captures the additional uncertainty coming from the interval censored dependent variable. The validity of the proposed method is validated by extensive model-based simulations.

Geographically weighted small area methods have been studied in literature for small area estimation. Although these approaches are useful for the estimation of small area means efficiently under strict parametric assumptions, they can be very sensitive to outliers in the data. In this paper, we propose a robust extension of the geographically weighted empirical best linear unbiased predictor (GWEBLUP). In particular, we introduce robust projective and predictive small area estimators under spatial non-stationarity. Mean squared error estimation is performed by two different analytic approaches that account for the spatial structure in the data. The results from the model- based simulations indicate that the proposed approach may lead to gains in terms of efficiency. Finally, the methodology is demonstrated in an illustrative application for estimating the average total cash costs for farms in Australia.

Modern systems of official statistics require the accurate and timely estimation of socio-demographic indicators for disaggregated geographical regions. Traditional data collection methods such as censuses or household surveys impose great financial and organizational burdens for National Statistical Institutes. The rise of new information and communication technologies offers promising sources to mitigate these shortcomings. In this paper we propose a unified approach for National Statistical Institutes based on small area estimation that allows for the estimation of socio-demographic indicators by using mobile phone data. In particular, the methodology is applied to mobile phone data from Senegal for deriving sub-national estimates of the share of illiterates disaggregated by gender. The estimates are used to identify hot spots of illiterates with a need for additional infrastructure or policy adjustments. Although the paper focuses on literacy as a particular socio-demographic indicator, the proposed approach is applicable to indicators from national statistics in general.

In this paper we will present recent work on a new unit-level small area methodology that can be used with continuous and discrete outcomes. The proposed method is based on constructing a model-based estimator of the distribution function by using a nested-error regression model for the quantiles of the target outcome. A general set of domain-specific parameters that extends beyond averages is then estimated by sampling from the estimated distribution function. For fitting the model we exploit the link between the Asymmetric Laplace Distribution and maximum likelihood estimation for quantile regression. The specification of the distribution of the random effects is considered in some detail by exploring the use of parametric and non- parametric alternatives. The use of the proposed methodology with discrete (count) outcomes requires appropriate transformations, in particular jittering. For the case of discrete outcomes the methodology relaxes the restrictive assumptions of the Poisson generalised linear mixed model and allows for what is potentially a more flexible mean-variance relationship. Mean Squared Error estimation is discussed. Extensive model-based simulations are used for comparing the proposed methodology to alternative unit-level methodologies for estimating a broad range of complex parameters.

Modern systems of official statistics require the estimation and publication of business statistics for disaggregated domains, for example, industry domains and geographical regions. Outlier robust methods have proven to be useful for small-area estimation. Recently proposed outlier robust model-based small-area methods assume, however, uncorrelated random effects. Spatial dependencies, resulting from similar industry domains or geographic regions, often occur. In this paper, we propose an outlier robust small-area methodology that allows for the presence of spatial correlation in the data. In particular, we present a robust predictive methodology that incorporates the potential spatial impact from other areas (domains) on the small area (domain) of interest. We further propose two parametric bootstrap methods for estimating the mean-squared error. Simulations indicate that the proposed methodology may lead to efficiency gains. The paper concludes with an illustrative application by using business data for estimating average labour costs in Italian provinces.

Arthroscopic treatment of hallux rigidus is appropriate after failed nonoperative treatment. Debridement with cheilectomy, and fusion are the main indications for arthroscopic treatment of hallux rigidus. If the cartilage damage is extensive and the patient has consented, then a fusion is performed at the same sitting.

Health-related quality of life assessment is important in the clinical evaluation of patients with metastatic disease that may offer useful information in understanding the clinical effectiveness of a treatment. To assess if a set of explicative variables impacts on the health-related quality of life, regression models are routinely adopted. However, the interest of researchers may be focussed on modelling other parts (e.g. quantiles) of this conditional distribution. In this paper we present an approach based on M-quantile regression to achieve this goal. We applied the proposed methodology to a prospective, randomized, multi-centre clinical trial. In order to take into account the hierarchical nature of the data we extended the M-quantile regression model to a three-level random effects specification and estimated it by maximum likelihood.

Objective: Fixed cavovarus deformity can lead to anteromedial ankle arthrosis due to elevated medial joint contact stresses. Lateralizing calcaneal osteotomies and tibial osteotomies are commonly used to treat symptoms and redistribute joint contact forces. In a former study a significant lateral shift[for full text, please go to the a.m. URL], Deutscher Kongress für Orthopädie und Unfallchirurgie (DKOU 2013)

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.