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Estimates of regression coefficients based on the sign covariance matrix

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  • Esa Ollila
  • Hannu Oja
  • Thomas P. Hettmansperger
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    Abstract

    A new estimator of the regression parameters is introduced in a multivariate multiple-regression model in which both the vector of explanatory variables and the vector of response variables are assumed to be random. The affine equivariant estimate matrix is constructed using the sign covariance matrix (SCM) where the sign concept is based on Oja's criterion function. The influence function and asymptotic theory are developed to consider robustness and limiting efficiencies of the SCM regression estimate. The estimate is shown to be consistent with a limiting multinormal distribution. The influence function, as a function of the length of the contamination vector, is shown to be linear in elliptic cases; for the least squares (LS) estimate it is quadratic. The asymptotic relative efficiencies with respect to the LS estimate are given in the multivariate normal as well as the "t"-distribution cases. The SCM regression estimate is highly efficient in the multivariate normal case and, for heavy-tailed distributions, it performs better than the LS estimate. Simulations are used to consider finite sample efficiencies with similar results. The theory is illustrated with an example. Copyright 2002 Royal Statistical Society.

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    Bibliographic Info

    Article provided by Royal Statistical Society in its journal Journal Of The Royal Statistical Society Series B.

    Volume (Year): 64 (2002)
    Issue (Month): 3 ()
    Pages: 447-466

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    Handle: RePEc:bla:jorssb:v:64:y:2002:i:3:p:447-466

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    Cited by:
    1. Agulló, Jose & Croux, Christophe & Van Aelst, Stefan, 2008. "The multivariate least-trimmed squares estimator," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 311-338, March.
    2. Jung, Kang-Mo, 2005. "Multivariate least-trimmed squares regression estimator," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 307-316, February.
    3. Hill, Jonathan B. & Aguilar, Mike, 2013. "Moment condition tests for heavy tailed time series," Journal of Econometrics, Elsevier, vol. 172(2), pages 255-274.
    4. 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.
    5. Ollila, Esa & Oja, Hannu & Croux, Christophe, 2003. "The affine equivariant sign covariance matrix: asymptotic behavior and efficiencies," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 328-355, November.
    6. Huo, Lijuan & Kim, Tae-Hwan & Kim, Yunmi, 2012. "Robust estimation of covariance and its application to portfolio optimization," Finance Research Letters, Elsevier, vol. 9(3), pages 121-134.
    7. Ella Roelant & Stefan Aelst, 2007. "An L1-type estimator of multivariate location and shape," Statistical Methods and Applications, Springer, vol. 15(3), pages 381-393, February.
    8. Roelant, E. & Van Aelst, S. & Croux, C., 2009. "Multivariate generalized S-estimators," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 876-887, May.

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