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On the robustness of two-stage estimators

Author

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  • Zhelonkin, Mikhail
  • Genton, Marc G.
  • Ronchetti, Elvezio

Abstract

The aim of this note is to provide a general framework for the analysis of the robustness properties of a broad class of two-stage models. We derive the influence function, the change-of-variance function, and the asymptotic variance of a general two-stage M-estimator, and provide their interpretations. We illustrate our results in the case of the two-stage maximum likelihood estimator and the two-stage least squares estimator.

Suggested Citation

  • Zhelonkin, Mikhail & Genton, Marc G. & Ronchetti, Elvezio, 2012. "On the robustness of two-stage estimators," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 726-732.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:4:p:726-732
    DOI: 10.1016/j.spl.2011.12.014
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    References listed on IDEAS

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    1. Christophe Muller & Tae-Hwan Kim, 2005. "Two-Stage Huber Estimation," Working Papers. Serie AD 2005-17, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    2. James W. Hardin, 2002. "The robust variance estimator for two-stage models," Stata Journal, StataCorp LLC, vol. 2(3), pages 253-266, August.
    3. Newey, Whitney K., 1984. "A method of moments interpretation of sequential estimators," Economics Letters, Elsevier, vol. 14(2-3), pages 201-206.
    4. Adrian Pagan, 1986. "Two Stage and Related Estimators and Their Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 517-538.
    5. Murphy, Kevin M & Topel, Robert H, 2002. "Estimation and Inference in Two-Step Econometric Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 88-97, January.
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    Cited by:

    1. Naghi, Andrea A. & Váradi, Máté & Zhelonkin, Mikhail, 2025. "Robust Estimation of Probit Models with Endogeneity," Econometrics and Statistics, Elsevier, vol. 34(C), pages 78-90.
    2. Cantoni, Eva & de Luna, Xavier, 2020. "Semiparametric inference with missing data: Robustness to outliers and model misspecification," Econometrics and Statistics, Elsevier, vol. 16(C), pages 108-120.
    3. Schumann, Martin & Tripathi, Gautam, 2018. "Convexity of probit weights," Statistics & Probability Letters, Elsevier, vol. 143(C), pages 81-85.
    4. Yei Eun Shin & Takumi Saegusa, 2024. "Nested case–control sampling without replacement," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 30(4), pages 776-799, October.
    5. Mikhail Zhelonkin & Marc G. Genton & Elvezio Ronchetti, 2016. "Robust inference in sample selection models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 805-827, September.
    6. Andrea A. Naghi & Máté Váradi & Mikhail Zhelonkin, 2021. "Robust Estimation of Probit Models with Endogeneity," Tinbergen Institute Discussion Papers 21-004/III, Tinbergen Institute.

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