A LAN based Neyman smooth test for Pareto distributions |
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Authors: | Michael Falk Armelle Guillou Gwladys Toulemonde |
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Affiliation: | 1. Institute of Mathematics, University of Würzburg, Am Hubland, D-97074 Würzburg, Germany;2. IRMA, Université Louis Pasteur, 7 rue René Descartes, F-67084 Strasbourg Cedex, France;3. LSTA, Université Pierre et Marie Curie, Bo?ˆte 158, 175 rue du chevaleret, F-75013 Paris, France |
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Abstract: | The Pareto distribution is found in a large number of real world situations and is also a well-known model for extreme events. In the spirit of Neyman [1937. Smooth tests for goodness of fit. Skand. Aktuarietidskr. 20, 149–199] and Thomas and Pierce [1979. Neyman's smooth goodness-of-fit test when the hypothesis is composite. J. Amer. Statist. Assoc. 74, 441–445], we propose a smooth goodness of fit test for the Pareto distribution family which is motivated by LeCam's theory of local asymptotic normality (LAN). We establish the behavior of the associated test statistic firstly under the null hypothesis that the sample follows a Pareto distribution and secondly under local alternatives using the LAN framework. Finally, simulations are provided in order to study the finite sample behavior of the test statistic. |
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Keywords: | 62F03 62F05 |
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