IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v115y2013icp359-373.html
   My bibliography  Save this article

Optimal robust M-estimators using Rényi pseudodistances

Author

Listed:
  • Toma, Aida
  • Leoni-Aubin, Samuela

Abstract

Using Rényi pseudodistances, new robustness and efficiency measures are defined. On the basis of these measures, new optimal robust M-estimators for multidimensional parameters, called optimal BRα-robust M-estimators, are derived using the Hampel’s infinitesimal approach. The classical optimal Bi-robust estimator is particularly obtained. It is shown that the new optimal estimators are characterized by equivariance properties: equivariance with respect to reparametrizations, as well as equivariance with respect to transformations of the data set when the model is generated by a group of transformations. The performance of these estimators is illustrated by Monte Carlo simulations in the case of the Weibull distribution, as well as on the basis of real data.

Suggested Citation

  • Toma, Aida & Leoni-Aubin, Samuela, 2013. "Optimal robust M-estimators using Rényi pseudodistances," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 359-373.
    • Handle: RePEc:eee:jmvana:v:115:y:2013:i:c:p:359-373
    DOI: 10.1016/j.jmva.2012.10.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X12002266
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2012.10.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Alfio Marazzi & Victor Yohai, 2010. "Optimal robust estimates using the Hellinger distance," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 4(2), pages 169-179, September.
    3. Helmut Rieder & Matthias Kohl & Peter Ruckdeschel, 2008. "The cost of not knowing the radius," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(1), pages 13-40, February.
    4. Filia Vonta & Kyriacos Mattheou & Alex Karagrigoriou, 2012. "On Properties of the (Φ, a)-Power Divergence Family with Applications in Goodness of Fit Tests," Methodology and Computing in Applied Probability, Springer, vol. 14(2), pages 335-356, June.
    5. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    6. Yohai, Victor J., 2008. "Optimal robust estimates using the Kullback-Leibler divergence," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1811-1816, September.
    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. Matthias Kohl & Peter Ruckdeschel & Helmut Rieder, 2010. "Infinitesimally Robust estimation in general smoothly parametrized models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(3), pages 333-354, August.
    9. Toma, Aida & Broniatowski, Michel, 2011. "Dual divergence estimators and tests: Robustness results," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 20-36, January.
    10. Kris Boudt & Derya Caliskan & Christophe Croux, 2011. "Robust explicit estimators of Weibull parameters," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(2), pages 187-209, March.
    11. Toma, Aida, 2009. "Optimal robust M-estimators using divergences," Statistics & Probability Letters, Elsevier, vol. 79(1), pages 1-5, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tsukuma, Hisayuki, 2014. "Minimax covariance estimation using commutator subgroup of lower triangular matrices," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 333-344.
    2. Diaa Al Mohamad, 2018. "Towards a better understanding of the dual representation of phi divergences," Statistical Papers, Springer, vol. 59(3), pages 1205-1253, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Diaa Al Mohamad, 2018. "Towards a better understanding of the dual representation of phi divergences," Statistical Papers, Springer, vol. 59(3), pages 1205-1253, September.
    2. Amor Keziou & Aida Toma, 2021. "A Robust Version of the Empirical Likelihood Estimator," Mathematics, MDPI, vol. 9(8), pages 1-19, April.
    3. Toma, Aida & Broniatowski, Michel, 2011. "Dual divergence estimators and tests: Robustness results," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 20-36, January.
    4. Chalabi, Yohan & Wuertz, Diethelm, 2012. "Portfolio optimization based on divergence measures," MPRA Paper 43332, University Library of Munich, Germany.
    5. Aida Toma & Samuela Leoni-Aubin, 2015. "Robust Portfolio Optimization Using Pseudodistances," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-26, October.
    6. Valdora, Marina & Yohai, Víctor, 2020. "M estimators based on the probability integral transformation with applications to count data," Statistics & Probability Letters, Elsevier, vol. 162(C).
    7. 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.
    8. Ronchetti, Elvezio, 2020. "Accurate and robust inference," Econometrics and Statistics, Elsevier, vol. 14(C), pages 74-88.
    9. 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.
    10. Gayen, Atin & Kumar, M. Ashok, 2021. "Projection theorems and estimating equations for power-law models," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    11. Ayanendranath Basu & Abhik Ghosh & Nirian Martin & Leandro Pardo, 2018. "Robust Wald-type tests for non-homogeneous observations based on the minimum density power divergence estimator," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(5), pages 493-522, July.
    12. 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).
    13. Broniatowski, Michel, 2014. "Minimum divergence estimators, maximum likelihood and exponential families," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 27-33.
    14. Kocięcki, Andrzej & Kolasa, Marcin, 2023. "A solution to the global identification problem in DSGE models," Journal of Econometrics, Elsevier, vol. 236(2).
    15. Carvalho Lopes, Celia Mendes & Bolfarine, Heleno, 2012. "Random effects in promotion time cure rate models," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 75-87, January.
    16. Orazio Attanasio & Sarah Cattan & Emla Fitzsimons & Costas Meghir & Marta Rubio-Codina, 2020. "Estimating the Production Function for Human Capital: Results from a Randomized Controlled Trial in Colombia," American Economic Review, American Economic Association, vol. 110(1), pages 48-85, January.
    17. Daeyoung Kim & Bruce Lindsay, 2015. "Empirical identifiability in finite mixture models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(4), pages 745-772, August.
    18. Andrew Chesher & Adam Rosen, 2015. "Characterizations of identified sets delivered by structural econometric models," CeMMAP working papers CWP63/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    19. Gary Koop & M. Hashem Pesaran & Ron P. Smith, 2013. "On Identification of Bayesian DSGE Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 300-314, July.
    20. M. Hashem Pesaran & Yongcheol Shin, 2002. "Long-Run Structural Modelling," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 49-87.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:115:y:2013:i:c:p:359-373. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.