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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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Bibliographic Info

Article provided by American Statistical Association in its journal Journal of the American Statistical Association.

Volume (Year): 103 (2008)
Issue (Month): (June)
Pages: 687-696

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Handle: RePEc:bes:jnlasa:v:103:y:2008:m:june:p:687-696

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  1. 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.
  2. Marc G. Genton & André Lucas, 2000. "Comprehensive Definitions of Breakdown-Points for Independent and Dependent Observations," Tinbergen Institute Discussion Papers 00-040/2, Tinbergen Institute.
  3. Hausman, J. A. & Abrevaya, Jason & Scott-Morton, F. M., 1998. "Misclassification of the dependent variable in a discrete-response setting," Journal of Econometrics, Elsevier, vol. 87(2), pages 239-269, September.
  4. Hadi, Ali S. & Luceno, Alberto, 1997. "Maximum trimmed likelihood estimators: a unified approach, examples, and algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 25(3), pages 251-272, August.
  5. Christmann, Andreas & Rousseeuw, Peter J., 2001. "Measuring overlap in binary regression," Computational Statistics & Data Analysis, Elsevier, vol. 37(1), pages 65-75, July.
  6. Cizek, P., 2007. "General Trimmed Estimation: Robust Approach to Nonlinear and Limited Dependent Variable Models (Replaces DP 2007-1)," Discussion Paper 2007-65, Tilburg University, Center for Economic Research.
  7. 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.
  8. Cizek, P., 2007. "General Trimmed Estimation: Robust Approach to Nonlinear and Limited Dependent Variable Models (Replaced by DP 2007-65)," Discussion Paper 2007-1, Tilburg University, Center for Economic Research.
  9. Croux, Christophe & Flandre, Cécile & Haesbroeck, Gentiane, 2002. "The breakdown behavior of the maximum likelihood estimator in the logistic regression model," Statistics & Probability Letters, Elsevier, vol. 60(4), pages 377-386, December.
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