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Small Area-Statistik: Methoden und Anwendungen

Small area statistics: methods and applications

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Zusammenfassung

Moderne Haushaltsstichproben sollen zunehmend reliable Informationen bezüglich inhaltlicher und geographischer Subgruppen liefern. Derartige Informationen werden im Allgemeinen alle zehn Jahre auf Basis von Volkszählungen gewonnen. In der aktuellen europäischen Zensus-Runde haben sich einige Länder dazu entschlossen, neue Methoden zu implementieren, welche keine vollständige Auszählung der Bevölkerung mehr benötigen.

Die Schweiz und Deutschland haben sich beispielsweise für einen sogenannten registergestützten Zensus entschieden. Dabei werden zunächst Melderegisterdaten ausgewertet. Mit Hilfe einer zusätzlichen Stichprobe werden weitere Informationen gewonnen, welche auch eine statistische Korrektur möglicher Registerfehler erlauben.

Dieser Paradigmenwechsel in der amtlichen Statistik erfordert aber auch eine adäquate Anpassung der statistischen Methodik. Bei Schätzungen in registergestützten Zensus interessieren dabei nicht nur die Kennwerte für die Gesamtpopulation in Deutschland, sondern auch für Kreise, Verbandsgemeinden und gegebenenfalls auch für Gemeinden; in der Schweiz analog für Kantone und Zählgemeinden.

Je nach Größe dieser Gebiete können sehr kleine Teilstichprobenumfänge auftreten, in denen klassische Schätzverfahren keine ausreichende Genauigkeit mehr garantieren. Moderne Small Area-Schätzmethoden können hier von Nutzen sein.

In der vorliegenden Arbeit sollen anhand geeigneter Anwendungsbeispiele aus der aktuellen Zensusforschung die Methoden und Konzepte der Small Area-Statistik motiviert und dargestellt werden. Neben der Einführung in die Basis-Modelle der Small Area-Statistik wird auch auf einige interessante Erweiterungen eingegangen. Die Methoden liefern gleichzeitig auch eine wesentliche Grundlage einer reliablen Regionalstatistik, welche präzise Statistiken für kleine Gebiete benötigt.

Abstract

Modern household surveys increasingly provide information on subgroups as defined by content or regions. This kind of information, in general, is gained from censuses every ten years. Within the current European census round, some countries have decided to implement new methods which do not rely on a complete enumeration of the population. Switzerland and Germany, for example, are applying a register-assisted census. An exploitation of the register of residents is enriched with information gained from an additional sample. This sample also furnishes possible statistical corrections of the register. This change of paradigm in official statistics urges for adequate statistical methods. In a register-assisted census, additionally to efficient estimates at national level, reliable regional estimates are required. However, the disaggregation may result in very low sample sizes for some of the areas of interest. Whilst classical design-based methods will not produce reliable estimates for these areas, modern model-based small area methods may improve the quality of the estimates by far. The present work focuses on illustrating the small area estimation concepts and methods by two examples of recent research on register-assisted censuses. Additionally to two basic small area models, various recent extensions will be discussed. The successful application of these methods is of crucial importance for obtaining reliable regionalized statistics.

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Danksagung

Die Autoren danken persönlich ganz herzlich Herrn Professor Dr. Hans Wolfgang Brachinger für die freundliche Einladung, Small Area-Methoden hier vorzustellen. So war es zu seiner Zeit als Herausgeber der Zeitschrift sein ausdrücklicher Wunsch, diese in Deutschland noch nicht so verbreiteten Methoden, welche beim Zensus 2011 in der Diskussion zur Anwendung standen, eingehend vorzustellen.

Ein besonderer Dank geht auch an die Statistischen Ämter des Bundes und der Länder in Deutschland sowie das Schweizer Bundesamt für Statistik, welche uns im Rahmen der Forschungsarbeiten zu beiden Zensus die Möglichkeit geschaffen haben, geeignete Methoden und Anwendungen weiter zu erforschen.

Ein Dank geht auch an die Forschungsinitiative des Landes Rheinland-Pfalz, welche uns im Rahmen des Forschungszentrums für Regional- und Umweltstatistik unterstützt. Gegenstand der Forschungsarbeiten sind die bereits erwähnten effizienten Algorithmen, das auf Kalibrierung basierende Benchmarking sowie Small Area-Methoden zur Waldinventur.

Danken möchten wir ebenso unseren Kollegen in den Projekten AMELI, BLUE-ETS und dem Partnerprojekt SAMPLE sowie den Kollegen im Zensus-Projekt sowie am Lehrstuhl für zahlreiche inspirierende Diskussionen rund um die Small Area-Statistik.

Schließlich danken wir ganz herzlich dem Associate Editor PD Dr. Siegfried Gabler, der sich dem Begutachtungsprozess dieses Artikels angenommen hat und zusammen mit zwei anonymen Gutachtern mit sehr wertvollen Hinweisen wesentlich zur besseren Lesbarkeit des Artikels beigetragen hat. Ebenso danken die Autoren Herrn Diplom-Volkswirt Florian Ertz für seine große Unterstützung bei der Harmonisierung der Begrifflichkeiten.

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  1. FB IV, VWL, Wirtschafts- und Sozialstatistik, Universität Trier, Universitätsring 15, 54296, Trier, Deutschland

    Ralf Münnich & Jan Pablo Burgard

  2. Dozent an der Eufom European University for Economics & Management A.s.b.l., 7, rue Alcide de Gasperi, 2981, Luxembourg-Kirchberg, Luxembourg

    Martin Vogt

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Münnich, R., Burgard, J.P. & Vogt, M. Small Area-Statistik: Methoden und Anwendungen. AStA Wirtsch Sozialstat Arch 6, 149–191 (2013). https://doi.org/10.1007/s11943-013-0126-1

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