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Influence analysis of robust Wald-type tests

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  • Ghosh, Abhik
  • Mandal, Abhijit
  • Martín, Nirian
  • Pardo, Leandro

Abstract

We consider a robust version of the classical Wald test statistics for testing simple and composite null hypotheses for general parametric models. These test statistics are based on the minimum density power divergence estimators instead of the maximum likelihood estimators. An extensive study of their robustness properties is given though the influence functions as well as the chi-square inflation factors. It is theoretically established that the level and power of these robust tests are stable against outliers, whereas the classical Wald test breaks down. Some numerical examples confirm the validity of the theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:147:y:2016:i:c:p:102-126
    DOI: 10.1016/j.jmva.2016.01.004
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    References listed on IDEAS

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    1. Ronchetti, Elvezio & Trojani, Fabio, 2001. "Robust inference with GMM estimators," Journal of Econometrics, Elsevier, vol. 101(1), pages 37-69, March.
    2. 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.
    3. Abhik Ghosh & Ayanendranath Basu, 2015. "Robust estimation for non-homogeneous data and the selection of the optimal tuning parameter: the density power divergence approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(9), pages 2056-2072, September.
    4. Toma, Aida & Broniatowski, Michel, 2011. "Dual divergence estimators and tests: Robustness results," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 20-36, January.
    5. Van Aelst, Stefan & Willems, Gert, 2011. "Robust and Efficient One-Way MANOVA Tests," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 706-718.
    6. Cantoni E. & Ronchetti E., 2001. "Robust Inference for Generalized Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1022-1030, 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. Wang, Lan & Qu, Annie, 2007. "Robust Tests in Regression Models With Omnibus Alternatives and Bounded Influence," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 347-358, March.
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    Cited by:

    1. Ayanendranath Basu & Abhik Ghosh & Abhijit Mandal & Nirian Martin & Leandro Pardo, 2021. "Robust Wald-type tests in GLM with random design based on minimum density power divergence estimators," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 973-1005, September.
    2. 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).
    3. Stephanie Aerts & Gentiane Haesbroeck, 2017. "Robust asymptotic tests for the equality of multivariate coefficients of variation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 163-187, March.
    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. Ayanendranath Basu & Abhijit Mandal & Nirian Martín & Leandro Pardo, 2019. "A Robust Wald-Type Test for Testing the Equality of Two Means from Log-Normal Samples," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 85-107, March.
    6. Abhik Ghosh, 2022. "Robust parametric inference for finite Markov chains," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 118-147, March.
    7. Elżbieta Szaruga & Elżbieta Załoga, 2022. "Qualitative–Quantitative Warning Modeling of Energy Consumption Processes in Inland Waterway Freight Transport on River Sections for Environmental Management," Energies, MDPI, vol. 15(13), pages 1-21, June.
    8. 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.

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