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Dual divergence estimators and tests: Robustness results

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  • Toma, Aida
  • Broniatowski, Michel

Abstract

The class of dual [phi]-divergence estimators (introduced in Broniatowski and Keziou (2009) [5]) is explored with respect to robustness through the influence function approach. For scale and location models, this class is investigated in terms of robustness and asymptotic relative efficiency. Some hypothesis tests based on dual divergence criteria are proposed and their robustness properties are studied. The empirical performances of these estimators and tests are illustrated by Monte Carlo simulation for both non-contaminated and contaminated data.

Suggested Citation

  • Toma, Aida & Broniatowski, Michel, 2011. "Dual divergence estimators and tests: Robustness results," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 20-36, January.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:1:p:20-36
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    References listed on IDEAS

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    1. Broniatowski, Michel & Keziou, Amor, 2009. "Parametric estimation and tests through divergences and the duality technique," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 16-36, January.
    2. Rosario Dell'Aquila & Elvezio Ronchetti, 2004. "Robust tests of predictive accuracy," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 161-184.
    3. Ayanendranath Basu & Bruce Lindsay, 1994. "Minimum disparity estimation for continuous models: Efficiency, distributions and robustness," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(4), pages 683-705, December.
    4. 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.
    5. Toma, Aida, 2009. "Optimal robust M-estimators using divergences," Statistics & Probability Letters, Elsevier, vol. 79(1), pages 1-5, January.
    6. Raúl Jiménz & Yongzhao Shao, 2001. "On robustness and efficiency of minimum divergence estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 241-248, December.
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    Citations

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    Cited by:

    1. Avijit Maji & Abhik Ghosh & Ayanendranath Basu, 2016. "The logarithmic super divergence and asymptotic inference properties," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(1), pages 99-131, January.
    2. Ghosh, Abhik & Basu, Ayanendranath, 2016. "Testing composite null hypotheses based on S-divergences," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 38-47.
    3. Broniatowski, Michel, 2014. "Minimum divergence estimators, maximum likelihood and exponential families," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 27-33.
    4. Toma, Aida & Leoni-Aubin, Samuela, 2013. "Optimal robust M-estimators using Rényi pseudodistances," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 359-373.
    5. Kang, Jiwon & Lee, Sangyeol, 2014. "Minimum density power divergence estimator for Poisson autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 44-56.
    6. Chalabi, Yohan & Wuertz, Diethelm, 2012. "Portfolio optimization based on divergence measures," MPRA Paper 43332, University Library of Munich, Germany.
    7. 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.

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