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Robust estimation for non-homogeneous data and the selection of the optimal tuning parameter: the density power divergence approach

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  • Abhik Ghosh
  • Ayanendranath Basu

Abstract

The density power divergence (DPD) measure, defined in terms of a single parameter α , has proved to be a popular tool in the area of robust estimation [1]. Recently, Ghosh and Basu [5] rigorously established the asymptotic properties of the MDPDEs in case of independent non-homogeneous observations. In this paper, we present an extensive numerical study to describe the performance of the method in the case of linear regression, the most common setup under the case of non-homogeneous data. In addition, we extend the existing methods for the selection of the optimal robustness tuning parameter from the case of independent and identically distributed (i.i.d.) data to the case of non-homogeneous observations. Proper selection of the tuning parameter is critical to the appropriateness of the resulting analysis. The selection of the optimal robustness tuning parameter is explored in the context of the linear regression problem with an extensive numerical study involving real and simulated data.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:42:y:2015:i:9:p:2056-2072
    DOI: 10.1080/02664763.2015.1016901
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    Citations

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    Cited by:

    1. E. Castilla & N. Martín & L. Pardo & K. Zografos, 2021. "Composite likelihood methods: Rao-type tests based on composite minimum density power divergence estimator," Statistical Papers, Springer, vol. 62(2), pages 1003-1041, April.
    2. 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.
    3. Elena Castilla & Nirian Martín & Leandro Pardo, 2018. "Minimum phi-divergence estimators for multinomial logistic regression with complex sample design," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(3), pages 381-411, July.
    4. Taranga Mukherjee & Abhijit Mandal & Ayanendranath Basu, 2019. "The B-exponential divergence and its generalizations with applications to parametric estimation," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(2), pages 241-257, June.
    5. Elena Castilla & Abhik Ghosh & Nirian Martin & Leandro Pardo, 2021. "Robust semiparametric inference for polytomous logistic regression with complex survey design," 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. 15(3), pages 701-734, September.
    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.

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