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Robust and Efficient Adaptive Estimation of Binary-Choice Regression Models

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  • Cizek, Pavel

Abstract

The binary-choice regression models such as probit and logit are used to describe the effect of explanatory variables on a binary response vari- able. Typically estimated by the maximum likelihood method, estimates are very sensitive to deviations from a model, such as heteroscedastic- ity and data contamination. At the same time, the traditional robust (high-breakdown point) methods such as the maximum trimmed like- lihood are not applicable since, by trimming observations, they induce the separation of data and non-identification of parameter estimates. To provide a robust estimation method for binary-choice regression, we con- sider a maximum symmetrically-trimmed likelihood estimator (MSTLE) and design a parameter-free adaptive procedure for choosing the amount of trimming. The proposed adaptive MSTLE preserves the robust prop- erties of the original MSTLE, significantly improves the infinite-sample behavior of MSTLE, and additionally, ensures asymptotic efficiency of the estimator under no contamination. The results concerning the trim- ming identification, robust properties, and asymptotic distribution of the proposed method are accompanied by simulation experiments and an application documenting the infinite-sample behavior of some existing and the proposed methods.
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(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Cizek, Pavel, 2008. "Robust and Efficient Adaptive Estimation of Binary-Choice Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 687-696, June.
    • Handle: RePEc:bes:jnlasa:v:103:y:2008:m:june:p:687-696
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    References listed on IDEAS

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    1. Christmann, Andreas & Rousseeuw, Peter J., 2001. "Measuring overlap in binary regression," Computational Statistics & Data Analysis, Elsevier, vol. 37(1), pages 65-75, July.
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    5. Peter Hall & Brett Presnell, 1999. "Biased Bootstrap Methods for Reducing the Effects of Contamination," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 661-680.
    6. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    7. Marc G. Genton & André Lucas, 2003. "Comprehensive definitions of breakdown points for independent and dependent observations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 81-94, February.
    8. Croux, Christophe & Haesbroeck, Gentiane, 2003. "Implementing the Bianco and Yohai estimator for logistic regression," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 273-295, October.
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    Cited by:

    1. Badi H. Baltagi & Georges Bresson, 2012. "A Robust Hausman–Taylor Estimator," Advances in Econometrics, in: Essays in Honor of Jerry Hausman, pages 175-214, Emerald Group Publishing Limited.
    2. Aquaro, M. & Čížek, P., 2013. "One-step robust estimation of fixed-effects panel data models," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 536-548.

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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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