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Comprehensive Definitions of Breakdown-Points for Independent and Dependent Observations

Author

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  • 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.

Suggested Citation

  • 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.
    • Handle: RePEc:tin:wpaper:20000040
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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.
    3. Yanyuan Ma & Marc G. Genton, 2000. "Highly Robust Estimation of the Autocovariance Function," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(6), pages 663-684, November.
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    Cited by:

    1. Cizek, P., 2005. "Trimmed Likelihood-based Estimation in Binary Regression Models," Discussion Paper 2005-108, Tilburg University, Center for Economic Research.
    2. Cizek, P., 2007. "General Trimmed Estimation : Robust Approach to Nonlinear and Limited Dependent Variable Models (Replaces DP 2007-1)," Other publications TiSEM eeccf622-dd18-41d4-a2f9-b, Tilburg University, School of Economics and Management.
    3. Alessio Farcomeni & Luca Greco, 2015. "S-estimation of hidden Markov models," Computational Statistics, Springer, vol. 30(1), pages 57-80, March.
    4. Cizek, P., 2009. "Generalized Methods of Trimmed Moments," Discussion Paper 2009-25, Tilburg University, Center for Economic Research.
    5. 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.
    6. 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 Science and Technology, Faculty of Management, vol. 25(1), pages 55-79.
    7. Čίžek, Pavel & Härdle, Wolfgang Karl, 2006. "Robust econometrics," SFB 649 Discussion Papers 2006-050, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    8. Cizek, P., 2007. "Efficient Robust Estimation of Time-Series Regression Models," Discussion Paper 2007-95, Tilburg University, Center for Economic Research.
    9. Lorenzo Camponovo & O. Scaillet & Fabio Trojani, 2013. "Predictability Hidden by Anomalous Observations," Swiss Finance Institute Research Paper Series 13-05, Swiss Finance Institute.
    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. Čížek, Pavel, 2012. "Semiparametric robust estimation of truncated and censored regression models," Journal of Econometrics, Elsevier, vol. 168(2), pages 347-366.
    12. 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.
    13. Tino Werner, 2023. "Quantitative robustness of instance ranking problems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(2), pages 335-368, April.
    14. Sally G. Arcidiacono & Damiano Rossello, 2022. "A hybrid approach to the discrepancy in financial performance’s robustness," Operational Research, Springer, vol. 22(5), pages 5441-5476, November.
    15. P. Čížek & M. Aquaro, 2018. "Robust estimation and moment selection in dynamic fixed-effects panel data models," Computational Statistics, Springer, vol. 33(2), pages 675-708, June.
    16. Luke A. Prendergast & Robert G. Staudte, 2017. "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. 15(3), pages 277-293, 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. Vicky Fasen‐Hartmann & Sebastian Kimmig, 2020. "Robust estimation of stationary continuous‐time arma models via indirect inference," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(5), pages 620-651, September.
    19. Cízek, Pavel, 2011. "Semiparametrically weighted robust estimation of regression models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 774-788, January.
    20. repec:hum:wpaper:sfb649dp2006-050 is not listed on IDEAS
    21. Jaakko Nevalainen & Denis Larocque & Hannu Oja, 2007. "A weighted spatial median for clustered data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 355-379, February.
    22. Genton, Mark G. & Ruiz-Gazen, Anne, 2009. "Visualizing Influential Observations in Dependent Data," TSE Working Papers 09-051, Toulouse School of Economics (TSE).
    23. Luke A. Prendergast & Robert G. Staudte, 2017. "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. 15(3), pages 277-293, September.
    24. Hella, Heikki, 2003. "On robust ESACF identification of mixed ARIMA models," Bank of Finland Scientific Monographs, Bank of Finland, volume 0, number sm2003_027, July.

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