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Testing statistical hypotheses based on the density power divergence

Author

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  • A. Basu
  • A. Mandal
  • N. Martin
  • L. Pardo

Abstract

The family of density power divergences is an useful class which generates robust parameter estimates with high efficiency. None of these divergences require any non-parametric density estimate to carry out the inference procedure. However, these divergences have so far not been used effectively in robust testing of hypotheses. In this paper, we develop tests of hypotheses based on this family of divergences. The asymptotic variances of the estimators are generally different from the inverse of the Fisher information matrix, so that the usual drop-in-divergence type statistics do not lead to standard Chi-square limits. It is shown that the alternative test statistics proposed herein have asymptotic limits which are described by linear combinations of Chi-square statistics. Extensive simulation results are presented to substantiate the theory developed. Copyright The Institute of Statistical Mathematics, Tokyo 2013

Suggested Citation

  • A. Basu & A. Mandal & N. Martin & L. Pardo, 2013. "Testing statistical hypotheses based on the density power divergence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(2), pages 319-348, April.
    • Handle: RePEc:spr:aistmt:v:65:y:2013:i:2:p:319-348
    DOI: 10.1007/s10463-012-0372-y
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    Citations

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    Cited by:

    1. Basu, Ayanendranath & Chakraborty, Soumya & Ghosh, Abhik & Pardo, Leandro, 2022. "Robust density power divergence based tests in multivariate analysis: A comparative overview of different approaches," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    2. A. Basu & A. Mandal & N. Martin & L. Pardo, 2018. "Testing Composite Hypothesis Based on the Density Power Divergence," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 222-262, November.
    3. Jingjing Wu & Rohana J. Karunamuni, 2018. "Efficient and robust tests for semiparametric models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(4), pages 761-788, August.
    4. Abhijit Mandal & Beste Hamiye Beyaztas & Soutir Bandyopadhyay, 2023. "Robust density power divergence estimates for panel data models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(5), pages 773-798, October.
    5. Avijit Maji & Abhik Ghosh & Ayanendranath Basu & Leandro Pardo, 2019. "Robust statistical inference based on the C-divergence family," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1289-1322, October.
    6. Ghosh, Abhik & Mandal, Abhijit & Martín, Nirian & Pardo, Leandro, 2016. "Influence analysis of robust Wald-type tests," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 102-126.
    7. Ghosh, Abhik & Basu, Ayanendranath, 2016. "Testing composite null hypotheses based on S-divergences," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 38-47.
    8. Byungsoo Kim & Junmo Song & Changryong Baek, 2021. "Robust test for structural instability in dynamic factor models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(4), pages 821-853, August.
    9. A. Basu & A. Mandal & N. Martin & L. Pardo, 2015. "Robust tests for the equality of two normal means based on the density power divergence," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(5), pages 611-634, July.
    10. Nirian Martín & Leandro Pardo, 2014. "Comments on: Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 279-282, June.

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