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A resampling design for computing high-breakdown regression

Author

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  • Rousseeuw, Peter J.

Abstract

For the computation of high-breakdown (HB) regression one typically uses an algorithm based on randomly selected p-subsets, where p is the number of parameters. This resampling algorithm may itself break down, with a probability that decreases with the number of p-subsets generated. In order to be certain that this algorithm does not break down, the number of p-subsets needs to be O(np). In this paper a resampling design is proposed such that for fixed p the necessary number of p-subsets is merely O(n). This resampling design can also be used for HB nonlinear regression and for HB estimators of multivariate location and scatter.

Suggested Citation

  • Rousseeuw, Peter J., 1993. "A resampling design for computing high-breakdown regression," Statistics & Probability Letters, Elsevier, vol. 18(2), pages 125-128, September.
    • Handle: RePEc:eee:stapro:v:18:y:1993:i:2:p:125-128
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    Cited by:

    1. Prieto, Francisco J., 1997. "Robust covariance matrix estimation and multivariate outlier detection," DES - Working Papers. Statistics and Econometrics. WS 10497, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Zuo, Yijun & Lai, Shaoyong, 2011. "Exact computation of bivariate projection depth and the Stahel-Donoho estimator," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1173-1179, March.
    3. Nolan, D., 1999. "On min-max majority and deepest points," Statistics & Probability Letters, Elsevier, vol. 43(4), pages 325-333, July.
    4. Shao, Wei & Zuo, Yijun, 2012. "Simulated annealing for higher dimensional projection depth," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4026-4036.
    5. Hadi, Ali S. & Luceno, Alberto, 1997. "Maximum trimmed likelihood estimators: a unified approach, examples, and algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 25(3), pages 251-272, August.

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