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Robust semiparametric inference for polytomous logistic regression with complex survey design

Author

Listed:
  • Elena Castilla

    (Complutense University of Madrid)

  • Abhik Ghosh

    (Indian Statistical Institute)

  • Nirian Martin

    (Actuarial Economics and Statistics, Complutense University of Madrid)

  • Leandro Pardo

    (Complutense University of Madrid)

Abstract

Analyzing polytomous response from a complex survey scheme, like stratified or cluster sampling is very crucial in several socio-economics applications. We present a class of minimum quasi weighted density power divergence estimators for the polytomous logistic regression model with such a complex survey. This family of semiparametric estimators is a robust generalization of the maximum quasi weighted likelihood estimator exploiting the advantages of the popular density power divergence measure. Accordingly robust estimators for the design effects are also derived. Using the new estimators, robust testing of general linear hypotheses on the regression coefficients are proposed. Their asymptotic distributions and robustness properties are theoretically studied and also empirically validated through a numerical example and an extensive Monte Carlo study.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:advdac:v:15:y:2021:i:3:d:10.1007_s11634-020-00430-7
    DOI: 10.1007/s11634-020-00430-7
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    References listed on IDEAS

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    4. 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.
    5. 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.
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    10. 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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