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Comprehensive definitions of breakdown points for independent and dependent observations

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  • Marc G. Genton
  • André Lucas

Abstract

Summary. 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.

Suggested Citation

  • 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, February.
    • Handle: RePEc:bla:jorssb:v:65:y:2003:i:1:p:81-94
    DOI: 10.1111/1467-9868.00373
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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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