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An L1-type estimator of multivariate location and shape

Author

Listed:
  • Ella Roelant

    (Ghent University - UGent)

  • Stefan Van Aelst

    (Ghent University - UGent)

Abstract

In this note we study a multivariate extension of the median obtained by considering the median as the L1 location estimator. Contrary to other multivariate extensions, this multivariate estimator yields simultaneously a location estimate and shape/scatter estimate. We investigate properties of the estimator such as the influence function and asymptotic variances and compare it with other estimators of location and shape.

Suggested Citation

  • Ella Roelant & Stefan Van Aelst, 2007. "An L1-type estimator of multivariate location and shape," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 381-393, February.
    • Handle: RePEc:spr:stmapp:v:15:y:2007:i:3:d:10.1007_s10260-006-0030-8
    DOI: 10.1007/s10260-006-0030-8
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    References listed on IDEAS

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    1. Thomas P. Hettmansperger, 2002. "A practical affine equivariant multivariate median," Biometrika, Biometrika Trust, vol. 89(4), pages 851-860, December.
    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:

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    2. Shi, Jianhong & Bai, Xiuqin & Song, Weixing, 2022. "Tweedie-type formulae for a multivariate Laplace distribution," Statistics & Probability Letters, Elsevier, vol. 183(C).
    3. G. Zioutas & C. Chatzinakos & T. D. Nguyen & L. Pitsoulis, 2017. "Optimization techniques for multivariate least trimmed absolute deviation estimation," Journal of Combinatorial Optimization, Springer, vol. 34(3), pages 781-797, October.
    4. Hlubinka, Daniel & Šiman, Miroslav, 2013. "On elliptical quantiles in the quantile regression setup," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 163-171.
    5. Daniel Hlubinka & Miroslav Šiman, 2015. "On generalized elliptical quantiles in the nonlinear quantile regression setup," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 249-264, June.
    6. Olcay Arslan, 2010. "An alternative multivariate skew Laplace distribution: properties and estimation," Statistical Papers, Springer, vol. 51(4), pages 865-887, December.

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