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The asymptotic covariance matrix of the Oja median

Author

Listed:
  • Nadar, M.
  • Hettmansperger, T. P.
  • Oja, H.

Abstract

The Oja median, based on a sample of multivariate data, is an affine equivariant estimate of the centre of the distribution. It reduces to the sample median in one dimension and has several nice robustness and efficiency properties. We develop different representations of its asymptotic variance and discuss ways to estimate this quantity. We consider symmetric multivariate models and also the more narrow elliptical models. A small simulation study is included to compare finite sample results to the asymptotic formulas.

Suggested Citation

  • Nadar, M. & Hettmansperger, T. P. & Oja, H., 2003. "The asymptotic covariance matrix of the Oja median," Statistics & Probability Letters, Elsevier, vol. 64(4), pages 431-442, October.
    • Handle: RePEc:eee:stapro:v:64:y:2003:i:4:p:431-442
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    References listed on IDEAS

    as
    1. Hannu Oja, 1999. "Affine Invariant Multivariate Sign and Rank Tests and Corresponding Estimates: a Review," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(3), pages 319-343, September.
    2. Oja, Hannu, 1983. "Descriptive statistics for multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 1(6), pages 327-332, October.
    3. Esa Ollila & Hannu Oja & Thomas P. Hettmansperger, 2002. "Estimates of regression coefficients based on the sign covariance matrix," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 447-466, August.
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    Cited by:

    1. Shen, Gang, 2008. "Asymptotics of Oja Median Estimate," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2137-2141, October.

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    More about this item

    Keywords

    Affine invariant Affine equivariant Multivariate median Multivariate L1 estimate;

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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