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Shrinkage Estimation of a Location Parameter for a Multivariate Skew Elliptic Distribution

Author

Listed:
  • Dominique Fourdrinier

    (Université de Normandie)

  • Tatsuya Kubokawa

    (Faculty of Economics)

  • William E. Strawderman

    (Department of Statistics and Biostatistics)

Abstract

The multivariate skew elliptic distributions include the multivariate skew-t distribution, which is represented as a mean- and scale-mixture distribution and is useful for analyzing skewed data with heavy tails. In the estimation of location parameters in the multivariate skew elliptic distributions, we derive minimax shrinkage estimators improving on the minimum risk location equivariant estimator relative to the quadratic loss function. Especially in the skew-t distribution, we suggest specific improved estimators where the conditions for their minimaxity do not depend on the degrees of freedom. We also study the case of a general elliptically symmetrical distribution when the covariance matrix is known up to an unknown multiple, but a residual vector is available to estimate the scale.

Suggested Citation

  • Dominique Fourdrinier & Tatsuya Kubokawa & William E. Strawderman, 2023. "Shrinkage Estimation of a Location Parameter for a Multivariate Skew Elliptic Distribution," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 808-828, February.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-022-00280-9
    DOI: 10.1007/s13171-022-00280-9
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    References listed on IDEAS

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    1. Cellier, D. & Fourdrinier, D., 1995. "Shrinkage Estimators under Spherical Symmetry for the General Linear Model," Journal of Multivariate Analysis, Elsevier, vol. 52(2), pages 338-351, February.
    2. Fourdrinier, Dominique & Strawderman, William E., 2008. "Generalized Bayes minimax estimators of location vectors for spherically symmetric distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(4), pages 735-750, April.
    3. Chou, Jine-Phone & Strawderman, William E., 1990. "Minimax estimation of means of multivariate normal mixtures," Journal of Multivariate Analysis, Elsevier, vol. 35(2), pages 141-150, November.
    4. Branco, Márcia D. & Dey, Dipak K., 2001. "A General Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 99-113, October.
    5. Strawderman, William E., 1974. "Minimax estimation of location parameters for certain spherically symmetric distributions," Journal of Multivariate Analysis, Elsevier, vol. 4(3), pages 255-264, September.
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