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Robust Estimation in Nonlinear Regression and Limited Dependent Variable Models

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Author Info
Pavel Cizek

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Abstract

Classical parametric estimation methods applied to nonlinear regression and limited-dependent-variable models are very sensitive to misspecification and data errors. This sensitivity is addressed by the theory of robust statistics which builds upon parametric specification, but provides methodology for designing misspecification-proof estimators by allowing for various "departures" of subsets of the data. However, this concept, developed in statistics, has so far been applied almost exclusively to linear regression models. Therefore, I adapt some robust methods, such as least trimmed squares, to nonlinear and limited-dependent-variable models. This paper presents the adapted robust estimators and proofs of their consistency. I also discuss several important examples of regression models which the proposed estimators can be applied to as well as suitable computational methods.

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Publisher Info
Paper provided by The Center for Economic Research and Graduate Education - Economic Institute, Prague in its series CERGE-EI Working Papers with number wp189.

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Date of creation: Dec 2001
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Handle: RePEc:cer:papers:wp189

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Related research
Keywords: least trimmed squares; limited-dependent-variable-models; nonlinear regression; robust estimation;

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models

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  1. Arabmazar, Abbas & Schmidt, Peter, 1981. "Further evidence on the robustness of the Tobit estimator to heteroskedasticity," Journal of Econometrics, Elsevier, vol. 17(2), pages 253-258, November. [Downloadable!] (restricted)
  2. Amemiya, Takeshi, 1983. "Non-linear regression models," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 6, pages 333-389 Elsevier. [Downloadable!] (restricted)
  3. Powell, James L, 1986. "Symmetrically Trimmed Least Squares Estimation for Tobit Models," Econometrica, Econometric Society, vol. 54(6), pages 1435-60, November. [Downloadable!] (restricted)
  4. Horowitz, Joel L., 1993. "Semiparametric estimation of a work-trip mode choice model," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 49-70, July. [Downloadable!] (restricted)
  5. Zaman, Asad & Rousseeuw, Peter J. & Orhan, Mehmet, 2001. "Econometric applications of high-breakdown robust regression techniques," Economics Letters, Elsevier, vol. 71(1), pages 1-8, April. [Downloadable!] (restricted)
  6. D. van Dijk & T. Terasvirta & P.H. Franses, 2000. "Smooth transition autoregressive models - A survey of recent developments," Econometric Institute Report 200, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
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  7. Wolfgang Hardle & Oliver Linton, 1994. "Applied Nonparametric Methods," Cowles Foundation Discussion Papers 1069, Cowles Foundation, Yale University. [Downloadable!]
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  8. Hurd, Michael, 1979. "Estimation in truncated samples when there is heteroscedasticity," Journal of Econometrics, Elsevier, vol. 11(2-3), pages 247-258. [Downloadable!] (restricted)
  9. Donald W.K. Andrews, 1986. "Consistency in Nonlinear Econometric Models: A Generic Uniform Law of Large Numbers," Cowles Foundation Discussion Papers 790, Cowles Foundation, Yale University. [Downloadable!]
  10. Arabmazar, Abbas & Schmidt, Peter, 1982. "An Investigation of the Robustness of the Tobit Estimator to Non-Normality," Econometrica, Econometric Society, vol. 50(4), pages 1055-63, July. [Downloadable!] (restricted)
  11. Pavel Cizek, 2001. "Robust Estimation with Discrete Explanatory Variables," CERGE-EI Working Papers wp183, The Center for Economic Research and Graduate Education - Economic Institute, Prague. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Cizek, Pavel, 2005. "Trimmed likelihood-based estimation in binary regression models," Discussion Paper 108, Tilburg University, Center for Economic Research. [Downloadable!]
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