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Minimum [phi]-divergence estimation in misspecified multinomial models

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  • Jiménez-Gamero, M.D.
  • Pino-Mejías, R.
  • Alba-Fernández, V.
  • Moreno-Rebollo, J.L.

Abstract

The consequences of model misspecification for multinomial data when using minimum [phi]-divergence or minimum disparity estimators to estimate the model parameters are considered. These estimators are shown to converge to a well-defined limit. Two applications of the results obtained are considered. First, it is proved that the bootstrap consistently estimates the null distribution of certain class of test statistics for model misspecification detection. Second, an application to the model selection test problem is studied. Both applications are illustrated with numerical examples.

Suggested Citation

  • Jiménez-Gamero, M.D. & Pino-Mejías, R. & Alba-Fernández, V. & Moreno-Rebollo, J.L., 2011. "Minimum [phi]-divergence estimation in misspecified multinomial models," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3365-3378, December.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:12:p:3365-3378
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    References listed on IDEAS

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    1. M. Jiménez-Gamero & A. Batsidis & M. Alba-Fernández, 2016. "Fourier methods for model selection," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(1), pages 105-133, February.

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