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Testing Composite Hypothesis Based on the Density Power Divergence

Author

Listed:
  • A. Basu

    (Indian Statistical Institute)

  • A. Mandal

    (Wayne State University)

  • N. Martin

    (Complutense University of Madrid)

  • L. Pardo

    (Complutense University of Madrid)

Abstract

In any parametric inference problem, the robustness of the procedure is a real concern. A procedure which retains a high degree of efficiency under the model and simultaneously provides stable inference under data contamination is preferable in any practical situation over another procedure which achieves its efficiency at the cost of robustness or vice versa. The density power divergence family of Basu et al. (Biometrika 85, 549–559 1998) provides a flexible class of divergences where the adjustment between efficiency and robustness is controlled by a single parameter β. In this paper we consider general tests of parametric hypotheses based on the density power divergence. We establish the asymptotic null distribution of the test statistic and explore its asymptotic power function. Numerical results illustrate the performance of the theory developed.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sankhb:v:80:y:2018:i:2:d:10.1007_s13571-017-0143-0
    DOI: 10.1007/s13571-017-0143-0
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    References listed on IDEAS

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    1. Ghosh, Abhik & Basu, Ayanendranath, 2016. "Testing composite null hypotheses based on S-divergences," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 38-47.
    2. J.J. Dik & M.C.M. de Gunst, 1985. "The Distribution Of General Quadratic Forms In Norma," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 39(1), pages 14-26, March.
    3. 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.
    4. 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.
    5. Martín, N. & Balakrishnan, N., 2013. "Hypothesis testing in a generic nesting framework for general distributions," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 1-23.
    6. Robert B. Davies, 1980. "The Distribution of a Linear Combination of χ2 Random Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(3), pages 323-333, November.
    7. Toma, Aida & Leoni-Aubin, Samuela, 2010. "Robust tests based on dual divergence estimators and saddlepoint approximations," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1143-1155, May.
    8. Toma, Aida & Broniatowski, Michel, 2011. "Dual divergence estimators and tests: Robustness results," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 20-36, January.
    9. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
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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. Ángel Felipe & María Jaenada & Pedro Miranda & Leandro Pardo, 2023. "Restricted Distance-Type Gaussian Estimators Based on Density Power Divergence and Their Applications in Hypothesis Testing," Mathematics, MDPI, vol. 11(6), pages 1-41, March.
    3. 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.

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