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The finite-sample breakdown point of the Oja bivariate median and of the corresponding half-samples version

Author

Listed:
  • Niinimaa, A.
  • Oja, H.
  • Tableman, Mara

Abstract

The purpose of this note is twofold. First it is shown that the finite-sample breakdown point of the bivariate median proposed by Oja (1983) is 2/(n + 2) which tends to zero rather than the previously conjectured . Then second, it is shown that applying a very general half-samples approach to the Oja criterion function leads to a class of estimators enjoying the 50% breakdown property and containing, as a special case, Rousseeuw's (1985, 1987) minimum covariance determinant estimator.

Suggested Citation

  • Niinimaa, A. & Oja, H. & Tableman, Mara, 1990. "The finite-sample breakdown point of the Oja bivariate median and of the corresponding half-samples version," Statistics & Probability Letters, Elsevier, vol. 10(4), pages 325-328, September.
    • Handle: RePEc:eee:stapro:v:10:y:1990:i:4:p:325-328
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    Citations

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    Cited by:

    1. Jin Wang & Weihua Zhou, 2015. "Effect of kurtosis on efficiency of some multivariate medians," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(3), pages 331-348, September.
    2. Hwang, Jinsoo & Jorn, Hongsuk & Kim, Jeankyung, 2004. "On the performance of bivariate robust location estimators under contamination," Computational Statistics & Data Analysis, Elsevier, vol. 44(4), pages 587-601, January.
    3. Marilena Furno, 2010. "A robust test of specification based on order statistics," Computational Statistics, Springer, vol. 25(4), pages 707-723, December.
    4. Hawkins, Douglas M. & Olive, David, 1999. "Applications and algorithms for least trimmed sum of absolute deviations regression," Computational Statistics & Data Analysis, Elsevier, vol. 32(2), pages 119-134, December.
    5. Kim, Jeankyung & Hwang, Jinsoo, 2001. "Asymptotic properties of location estimators based on projection depth," Statistics & Probability Letters, Elsevier, vol. 55(3), pages 293-299, December.
    6. Chakraborty, Biman & Chaudhuri, Probal, 1999. "A note on the robustness of multivariate medians," Statistics & Probability Letters, Elsevier, vol. 45(3), pages 269-276, November.

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