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Disparitätsmessung aus klassierten Daten mittels Schätzung von entropiemaximalen Dichtefunktionen

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  • Lucas, André

Abstract

Standardmethoden zur Schätzung von Disparitätsmaßen aus klassierten Daten basieren entweder auf der Bestimmung von Schranken, die den wahren Wert des jeweiligen Disparitätsmaßes einschließen (nichtparametrischer Ansatz) oder aber auf Annahmen bezüglich der den Daten zugrunde liegenden Verteilung, deren Parameter geschätzt werden müssen (parametrischer Ansatz). Die Parameterschätzung kann je nach angenommener Verteilung numerisch aufwendig sein und es ist nicht in jedem Fall gesichert, dass diese Verteilung eine gute Anpassung an die Daten darstellt. Die Bestimmung der Schranken ist hingegen nur dann sinnvoll, wenn diese nahe genug beieinander liegen (dies ist zumeist nur bei Vorliegen einer größeren Anzahl von Klassen der Fall). In diesem Beitrag wird die Schatzung von Disparitätsmaßen mittels Bestimmung von entropiemaximalen Dichtefunktionen dargestellt. Dabei wird in jeder Klasse die Entropie der geschätzten Dichtefunktion maximiert. Die durchgeführte Simulationsstudie bestätigt eine verbesserte Schätzung bei einem akzeptablen numerischen Aufwand auch bei einer kleinen Klassenanzahl.

Suggested Citation

  • Lucas, André, 1999. "Disparitätsmessung aus klassierten Daten mittels Schätzung von entropiemaximalen Dichtefunktionen," Discussion Papers in Econometrics and Statistics 1/99, University of Cologne, Institute of Econometrics and Statistics.
  • Handle: RePEc:zbw:ucdpse:199
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    References listed on IDEAS

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    2. Foster, James E., 1983. "An axiomatic characterization of the Theil measure of income inequality," Journal of Economic Theory, Elsevier, vol. 31(1), pages 105-121, October.
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    More about this item

    Keywords

    Maximum-entropy; density estimation; inequality measures; grouped data;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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