IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v213y2024ics016771522400155x.html

Bayes minimax estimator of the mean vector in an elliptically contoured distribution

Author

Listed:
  • Jiang, Jie
  • Wang, Lichun

Abstract

This paper investigates the Bayes estimator of the mean of an elliptically contoured distribution with unknown scale parameter under the quadratic loss. The Laplace transform and inverse Laplace transform of density facilitate us to obtain the expression of Bayes estimator. Then we prove the minimaxity of the Bayes estimator under certain conditions.

Suggested Citation

  • Jiang, Jie & Wang, Lichun, 2024. "Bayes minimax estimator of the mean vector in an elliptically contoured distribution," Statistics & Probability Letters, Elsevier, vol. 213(C).
    • Handle: RePEc:eee:stapro:v:213:y:2024:i:c:s016771522400155x
    DOI: 10.1016/j.spl.2024.110186
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016771522400155X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2024.110186?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Dominique Fourdrinier & Othmane Kortbi & William Strawderman, 2014. "Generalized Bayes minimax estimators of location vectors for spherically symmetric distributions with residual vector," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(2), pages 285-296, February.
    2. Osiewalski, Jacek & Steel, Mark F. J., 1993. "Robust bayesian inference in elliptical regression models," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 345-363.
    3. Chib, Siddhartha & Tiwari, Ram C. & Jammalamadaka, S. Rao, 1988. "Bayes prediction in regressions with elliptical errors," Journal of Econometrics, Elsevier, vol. 38(3), pages 349-360, July.
    4. Fourdrinier, Dominique & Kortbi, Othmane & Strawderman, William E., 2008. "Bayes minimax estimators of the mean of a scale mixture of multivariate normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(1), pages 74-93, January.
    5. Kubokawa, T. & Srivastava, M. S., 2001. "Robust Improvement in Estimation of a Mean Matrix in an Elliptically Contoured Distribution," Journal of Multivariate Analysis, Elsevier, vol. 76(1), pages 138-152, January.
    6. Zinodiny, S. & Rezaei, S. & Arjmand, O. Naghshineh & Nadarajah, S., 2013. "Bayes minimax estimation of the multivariate normal mean vector under quadratic loss functions," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2052-2056.
    7. Fang, Kai-Tai & Li, Runze, 1999. "Bayesian Statistical Inference on Elliptical Matrix Distributions," Journal of Multivariate Analysis, Elsevier, vol. 70(1), pages 66-85, July.
    8. Wells, Martin T. & Zhou, Gongfu, 2008. "Generalized Bayes minimax estimators of the mean of multivariate normal distribution with unknown variance," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2208-2220, November.
    9. Xu, Jian-Lun & Izmirlian, Grant, 2006. "Estimation of location parameters for spherically symmetric distributions," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 514-525, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Liu, Jin Shan & Ip, Wai Cheung & Wong, Heung, 2009. "Predictive inference for singular multivariate elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1440-1446, August.
    2. Kibria, B.M. Golam, 2006. "The matrix-t distribution and its applications in predictive inference," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 785-795, March.
    3. Zinodiny, S. & Rezaei, S. & Nadarajah, S., 2014. "Bayes minimax estimation of the multivariate normal mean vector under balanced loss function," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 96-101.
    4. Zinodiny, S. & Strawderman, W.E. & Parsian, A., 2011. "Bayes minimax estimation of the multivariate normal mean vector for the case of common unknown variance," Journal of Multivariate Analysis, Elsevier, vol. 102(9), pages 1256-1262, October.
    5. Kim, Hyoung-Moon & Mallick, Bani K., 2003. "A note on Bayesian spatial prediction using the elliptical distribution," Statistics & Probability Letters, Elsevier, vol. 64(3), pages 271-276, September.
    6. Maruyama, Yuzo & Strawderman, William E., 2009. "An extended class of minimax generalized Bayes estimators of regression coefficients," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2155-2166, November.
    7. Russo, Cibele M. & Paula, Gilberto A. & Aoki, Reiko, 2009. "Influence diagnostics in nonlinear mixed-effects elliptical models," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4143-4156, October.
    8. Jacek Osiewalski, 1999. "Bayesian analysis of nonlinear regression with equicorrelated elliptical errors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(2), pages 339-344, December.
    9. Dominique Fourdrinier & Othmane Kortbi & William Strawderman, 2014. "Generalized Bayes minimax estimators of location vectors for spherically symmetric distributions with residual vector," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(2), pages 285-296, February.
    10. Fourdrinier, Dominique & Strawderman, William E., 2016. "Stokes’ theorem, Stein’s identity and completeness," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 224-231.
    11. Aurélie Boisbunon & Stéphane Canu & Dominique Fourdrinier & William Strawderman & Martin T. Wells, 2014. "Akaike's Information Criterion, C p and Estimators of Loss for Elliptically Symmetric Distributions," International Statistical Review, International Statistical Institute, vol. 82(3), pages 422-439, December.
    12. Osiewalski, J. & Steel, M.F.J., 1989. "A Bayesian analysis of exogeneity in models pooling time-series and cross-section data," Discussion Paper 1989-14, Tilburg University, Center for Economic Research.
    13. Shokofeh Zinodiny & Saralees Nadarajah, 2023. "Generalized Bayes Minimax Estimators of the Variance of a Multivariate Normal Distribution," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1667-1683, August.
    14. Maruyama Yuzo, 2003. "A robust generalized Bayes estimator improving on the James-Stein estimator for spherically symmetric distributions," Statistics & Risk Modeling, De Gruyter, vol. 21(1), pages 69-78, January.
    15. Nadarajah Saralees, 2007. "A Truncated Bivariate t Distribution," Stochastics and Quality Control, De Gruyter, vol. 22(2), pages 303-313, January.
    16. Tsukuma, Hisayuki, 2010. "Shrinkage priors for Bayesian estimation of the mean matrix in an elliptically contoured distribution," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1483-1492, July.
    17. Arellano-Valle, R.B. & del Pino, G. & Iglesias, P., 2006. "Bayesian inference in spherical linear models: robustness and conjugate analysis," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 179-197, January.
    18. Chung, Hee Cheol & Ahn, Jeongyoun, 2021. "Subspace rotations for high-dimensional outlier detection," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    19. Osiewalski, Jacek & Welfe, Aleksander, 1997. "The Price-Wage Mechanism in Poland: An Endogenous Switching Model," Economic Change and Restructuring, Springer, vol. 30(2-3), pages 205-220.
    20. Phillips, Peter C. B., 1988. "Conditional and unconditional statistical independence," Journal of Econometrics, Elsevier, vol. 38(3), pages 341-348, July.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:213:y:2024:i:c:s016771522400155x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.