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Comprehensive definitions of breakdown points for independent and dependent observations

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  • Marc G. Genton
  • André Lucas

Abstract

We provide a new definition of breakdown in finite samples, with an extension to asymptotic breakdown. Previous definitions centre on defining a critical region for either the parameter or the objective function. If for a particular outlier configuration the critical region is entered, breakdown is said to occur. In contrast with the traditional approach, we leave the definition of the critical region implicit. Our proposal encompasses previous definitions of breakdown in linear and non-linear regression settings. In some cases, it leads to a different and more intuitive notion of breakdown than other procedures that are available. An important advantage of our new definition is that it also applies to models for dependent observations where current definitions of breakdown typically fail. We illustrate our suggestion by using examples from linear and non-linear regression, and time series. Copyright 2003 Royal Statistical Society.

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  • 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.
  • Handle: RePEc:bla:jorssb:v:65:y:2003:i:1:p:81-94
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    References listed on IDEAS

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    1. He, Xuming, 1991. "A local breakdown property of robust tests in linear regression," Journal of Multivariate Analysis, Elsevier, vol. 38(2), pages 294-305, August.
    2. Shinichi Sakata & Halbert White, 1998. "High Breakdown Point Conditional Dispersion Estimation with Application to S&P 500 Daily Returns Volatility," Econometrica, Econometric Society, vol. 66(3), pages 529-568, May.
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    Cited by:

    1. 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.
    2. repec:kap:jecinq:v:15:y:2017:i:3:d:10.1007_s10888-017-9347-9 is not listed on IDEAS
    3. Alessio Farcomeni & Luca Greco, 2015. "S-estimation of hidden Markov models," Computational Statistics, Springer, vol. 30(1), pages 57-80, March.
    4. Luke A. Prendergast & Robert G. Staudte, 0. "When large n is not enough – Distribution-free interval estimators for ratios of quantiles," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 0, pages 1-17.
    5. Cizek, P., 2005. "Trimmed Likelihood-based Estimation in Binary Regression Models," Discussion Paper 2005-108, Tilburg University, Center for Economic Research.
    6. Cízek, Pavel, 2011. "Semiparametrically weighted robust estimation of regression models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 774-788, January.
    7. Cizek, P., 2009. "Generalized Methods of Trimmed Moments," Discussion Paper 2009-25, Tilburg University, Center for Economic Research.
    8. Čížek, Pavel, 2012. "Semiparametric robust estimation of truncated and censored regression models," Journal of Econometrics, Elsevier, vol. 168(2), pages 347-366.
    9. Daniel Kosiorowski, 2015. "Two procedures for robust monitoring of probability distributions of economic data stream induced by depth functions," Operations Research and Decisions, Wroclaw University of Technology, Institute of Organization and Management, vol. 1, pages 55-79.
    10. 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.
    11. Cizek, P. & Aquaro, M., 2015. "Robust Estimation and Moment Selection in Dynamic Fixed-effects Panel Data Models," Discussion Paper 2015-002, Tilburg University, Center for Economic Research.
    12. Pavel Cizek & Wolfgang Härdle, 2006. "Robust Econometrics," SFB 649 Discussion Papers SFB649DP2006-050, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    13. Genton, Mark G. & Ruiz-Gazen, Anne, 2009. "Visualizing Influential Observations in Dependent Data," TSE Working Papers 09-051, Toulouse School of Economics (TSE).
    14. Lorenzo Camponovo & Olivier Scaillet & Fabio Trojani, 2018. "Predictability Hidden by Anomalous Observations," School of Economics Discussion Papers 0418, School of Economics, University of Surrey.
    15. Lorenzo Camponovo & Olivier Scaillet & Fabio Trojani, 2016. "Predictability Hidden by Anomalous Observations," Papers 1612.05072, arXiv.org.
    16. Pavel Čížek, 2013. "Reweighted least trimmed squares: an alternative to one-step estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 514-533, September.
    17. 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.
    18. Cizek, P., 2007. "Efficient Robust Estimation of Time-Series Regression Models," Discussion Paper 2007-95, Tilburg University, Center for Economic Research.

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