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Comprehensive Definitions of Breakdown-Points for Independent and Dependent Observations

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Author Info

  • Marc G. Genton

    (Massachusetts Institute of Technology)

  • André Lucas

    ()
    (Vrije Universiteit Amsterdam)

Abstract

We provide a new definition of breakdown in finite samples with an extension to asymptotic breakdown. Previous definitions center around defining a critical region for either the parameter or the objective function. If for a particular outlier constellation the critical region is entered, breakdown is said to occur. In contract to the traditional approach, we leave the definition of the critical region implicit. Our definition encompasses all previousdefinitions of breakdown in both linear and non-linear regression settings. Insome cases, it leads to a different notion of breakdown than other procedures available. An advantage is that our new definition also applied to models for dependent observations (time-series, spatial statistics) where currenty breakdown definitions typically fail. We illustrate our points using examples from linear and non-linear regression as well as time-series and spatial statistics.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 00-040/2.

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Date of creation: 12 May 2000
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Handle: RePEc:dgr:uvatin:20000040

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Web page: http://www.tinbergen.nl

Related research

Keywords: Bias curve; Linear regression; Non-linear regression; Outliers; Spatial statistics; Statistical robustness; Time series;

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Cited by:
  1. Genton, Mark G. & Ruiz-Gazen, Anne, 2009. "Visualizing Influential Observations in Dependent Data," TSE Working Papers, Toulouse School of Economics (TSE) 09-051, Toulouse School of Economics (TSE).
  2. Cizek, P., 2007. "General Trimmed Estimation: Robust Approach to Nonlinear and Limited Dependent Variable Models (Replaces DP 2007-1)," Discussion Paper, Tilburg University, Center for Economic Research 2007-65, Tilburg University, Center for Economic Research.
  3. Čížek, Pavel, 2012. "Semiparametric robust estimation of truncated and censored regression models," Journal of Econometrics, Elsevier, Elsevier, vol. 168(2), pages 347-366.
  4. Croux, Christophe & Flandre, Cécile & Haesbroeck, Gentiane, 2002. "The breakdown behavior of the maximum likelihood estimator in the logistic regression model," Statistics & Probability Letters, Elsevier, Elsevier, vol. 60(4), pages 377-386, December.
  5. Cízek, Pavel, 2011. "Semiparametrically weighted robust estimation of regression models," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 55(1), pages 774-788, January.
  6. Aquaro, M. & Čížek, P., 2013. "One-step robust estimation of fixed-effects panel data models," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 57(1), pages 536-548.
  7. Cizek, P., 2007. "General Trimmed Estimation: Robust Approach to Nonlinear and Limited Dependent Variable Models (Replaced by DP 2007-65)," Discussion Paper, Tilburg University, Center for Economic Research 2007-1, Tilburg University, Center for Economic Research.
  8. Cizek, P., 2005. "Trimmed Likelihood-based Estimation in Binary Regression Models," Discussion Paper, Tilburg University, Center for Economic Research 2005-108, Tilburg University, Center for Economic Research.
  9. Cizek, P., 2007. "Robust and Efficient Adaptive Estimation of Binary-Choice Regression Models," Discussion Paper, Tilburg University, Center for Economic Research 2007-12, Tilburg University, Center for Economic Research.
  10. Cizek, P., 2006. "Efficient Robust Estimation of Regression Models (Replaced by DP 2007-87)," Discussion Paper, Tilburg University, Center for Economic Research 2006-8, Tilburg University, Center for Economic Research.
  11. Pavel Cizek & Wolfgang Härdle, 2006. "Robust Econometrics," SFB 649 Discussion Papers SFB649DP2006-050, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  12. Cizek, P., 2009. "Generalized Methods of Trimmed Moments," Discussion Paper, Tilburg University, Center for Economic Research 2009-25, Tilburg University, Center for Economic Research.

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