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Disparitätsmessung aus klassierten Daten mittels Schätzung von entropiemaximalen Dichtefunktionen

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  • Lucas, André
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    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. -- Standard methods of inequality measurement from grouped data are usually based on the determination of bounds which enclose the true value of the inequality measure (nonparametric method), or on assumptions on the data generating distribution, for which it is necessary to estimate the parameters (parametric method). Estimating parameters for some distributions can cause great numerical efforts and it is not for sure, that the chosen distribution fits the data adequatly. On the other hand, the determination of bounds is only useful and practical if these bounds are close enough (this is usually the case only, if the data is divided in many groups). The aim of this paper is to present a method for estimating inequality measures, based on the estimation of distribution with the maximum-entropy method. With given data, the entropy of the estimated distribution in each group is maximized. Simulations confirm that this method is increasing the accuracy of the estimation, even with little number of groups and with an acceptable numerical effort.

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    Bibliographic Info

    Paper provided by University of Cologne, Department for Economic and Social Statistics in its series Discussion Papers in Statistics and Econometrics with number 1/99.

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    Date of creation: 1999
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    Handle: RePEc:zbw:ucdpse:199

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    Keywords: Maximum-entropy; density estimation; inequality measures; grouped data;

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    1. Gastwirth, Joseph L, 1972. "The Estimation of the Lorenz Curve and Gini Index," The Review of Economics and Statistics, MIT Press, vol. 54(3), pages 306-16, August.
    2. Foster, James E., 1983. "An axiomatic characterization of the Theil measure of income inequality," Journal of Economic Theory, Elsevier, Elsevier, vol. 31(1), pages 105-121, October.
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