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Testing Mixed Distributions when the Mixing Distribution Is Known

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Advances in Data Analysis, Data Handling and Business Intelligence

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Abstract

In this paper we present smooth goodness of fit tests for testing the mixture distribution of a sequence of i.i.d. random variables. We consider mixture models when the mixing distribution is known. We adapt a Schwarz’s criteria initiated by Ledwina (J Am Stat Assoc 89:1000–1005, 1994) and inspired by the Neyman (Skandinavian Aktuarial 20:149–199, 1937) smooth test procedure. A Monte Carlo study is provided in order to assess the performance of the test.

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References

  • Abramowitz, M., & Stegun I. A. (1972). Handbook of mathematical functions. New York: Dover.

    MATH  Google Scholar 

  • Ash, R. B., & Gardner, M. F. (1975). Topics in stochastics processes. New York: Academic.

    Google Scholar 

  • Azais, J. M., Gassiat, E., & Mercadier, C. (2009). The likelihood ratio test for general mixture models with or without structural parameter. ESAIM: Probability and Statistics, 13, 301–327.

    Article  MATH  MathSciNet  Google Scholar 

  • Cardot, H., Ferraty, F., & Sarda, P. (2003). Spline estimators for the functional linear model. Statistica Sinica, 13, 571–591.

    MATH  MathSciNet  Google Scholar 

  • Garel, B. (2005). Asymptotic theory of the likelihood ratio test for the identification of a mixture. Journal of Statistical Planning and Inference, 131, 271–296.

    Article  MATH  MathSciNet  Google Scholar 

  • Kallenberg, W. C. M., & Ledwina, T. (1995). Consistency and Monte Carlo simulation of data driven version of smooth goodness of fit tests. Annals of Statistics, 23, 1594–1608.

    Article  MATH  MathSciNet  Google Scholar 

  • Ledwina, T. (1994). Data-driven version of Neyman’s smooth test of fit. Journal of the American Statistical Association, 89, 1000–1005.

    Article  MATH  MathSciNet  Google Scholar 

  • Neyman, J. (1937). Smooth test for goodness of fit. Skandinavian Aktuarial, 20, 149–199.

    MATH  Google Scholar 

  • Pons, O. (2008). Asymptotic distributions in finite semi-parametric mixture models. ESAIM: Probability and Statistics, (forthcoming).

    Google Scholar 

  • Rayner, J. C. W., & Best, D. J. (1989). Smooth tests of goodness of fit. New York: Oxford University Press.

    MATH  Google Scholar 

  • Young R. M. (1991). Euler’s constant. Mathematical Gazette, 75, 187–190.

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Institut de Mathématiques de Luminy, Case 901, Université d’Aix-Marseille II, 13288, Marseille Cedex 9, France

    Denys Pommeret

Authors
  1. Denys Pommeret
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Correspondence to Denys Pommeret .

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Editors and Affiliations

  1. Universität der Bundeswehr, Fak. Wirtschafts-/Sozialwissenschaften, Helmut-Schmidt-Universität, Holstenhofweg 85, Hamburg, 22043, Germany

    Andreas Fink

  2. Dept. Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester, CO4 3SQ, United Kingdom

    Berthold Lausen

  3. Universität der Bundeswehr, Fak. Wirtschafts-/Sozialwissenschaften, Helmut-Schmidt-Universität, Holstenhofweg 85, Hamburg, 22043, Germany

    Wilfried Seidel

  4. FB 12 Mathematik und Informatik, Datenbionik AG, Universität Marburg, Hans-Meerwein-Straße, Marburg, 35032, Germany

    Alfred Ultsch

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© 2009 Springer-Verlag Berlin Heidelberg

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Pommeret, D. (2009). Testing Mixed Distributions when the Mixing Distribution Is Known. In: Fink, A., Lausen, B., Seidel, W., Ultsch, A. (eds) Advances in Data Analysis, Data Handling and Business Intelligence. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01044-6_23

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