IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v122y2013icp190-201.html
   My bibliography  Save this article

On extension of some identities for the bias and risk functions in elliptically contoured distributions

Author

Listed:
  • Nkurunziza, Sévérien
  • Chen, Fuqi

Abstract

In this paper, we are interested in an estimation problem concerning the mean parameter of a random matrix whose distribution is elliptically contoured. We derive two general formulas for the bias and risk functions of a class of multidimensional shrinkage-type estimators. As a by product, we generalize some recent identities established in Gaussian sample cases for which the shrinking random part is a single Kronecker-product. Here, the variance–covariance matrix of the shrinking random part is the sum of two Kronecker-products.

Suggested Citation

  • Nkurunziza, Sévérien & Chen, Fuqi, 2013. "On extension of some identities for the bias and risk functions in elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 190-201.
    • Handle: RePEc:eee:jmvana:v:122:y:2013:i:c:p:190-201
    DOI: 10.1016/j.jmva.2013.07.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X13001371
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2013.07.005?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Zinoviy Landsman & Emiliano Valdez, 2003. "Tail Conditional Expectations for Elliptical Distributions," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 55-71.
    2. Furman, Edward & Landsman, Zinoviy, 2006. "Tail Variance Premium with Applications for Elliptical Portfolio of Risks," ASTIN Bulletin, Cambridge University Press, vol. 36(2), pages 433-462, November.
    3. Sévérien Nkurunziza & S. Ejaz Ahmed, 2011. "Estimation strategies for the regression coefficient parameter matrix in multivariate multiple regression," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 65(4), pages 387-406, November.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Shakhawat Hossain & Le An Lac, 2021. "Optimal shrinkage estimations in partially linear single-index models for binary longitudinal data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 811-835, December.
    2. Sévérien Nkurunziza & Lei Shen, 2020. "Inference in a multivariate generalized mean-reverting process with a change-point," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 199-226, April.

    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. Landsman, Zinoviy & Makov, Udi & Shushi, Tomer, 2016. "Tail conditional moments for elliptical and log-elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 179-188.
    2. Fouad Marri & Khouzeima Moutanabbir, 2021. "Risk aggregation and capital allocation using a new generalized Archimedean copula," Papers 2103.10989, arXiv.org.
    3. Furman, Edward & Wang, Ruodu & Zitikis, Ričardas, 2017. "Gini-type measures of risk and variability: Gini shortfall, capital allocations, and heavy-tailed risks," Journal of Banking & Finance, Elsevier, vol. 83(C), pages 70-84.
    4. Fouad Marri & Khouzeima Moutanabbir, 2021. "Risk aggregation and capital allocation using a new generalized Archimedean copula," Working Papers hal-03169291, HAL.
    5. Shushi, Tomer, 2019. "The Minkowski length of a spherical random vector," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 104-107.
    6. Landsman, Zinoviy & Makov, Udi & Shushi, Tomer, 2018. "A multivariate tail covariance measure for elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 27-35.
    7. Baishuai Zuo & Chuancun Yin & Jing Yao, 2023. "Multivariate range Value-at-Risk and covariance risk measures for elliptical and log-elliptical distributions," Papers 2305.09097, arXiv.org.
    8. Jaworski, Piotr & Pitera, Marcin, 2017. "A note on conditional covariance matrices for elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 230-235.
    9. Landsman, Zinoviy & Pat, Nika & Dhaene, Jan, 2013. "Tail Variance premiums for log-elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 441-447.
    10. Piotr Jaworski & Marcin Pitera, 2017. "A note on conditional covariance matrices for elliptical distributions," Papers 1703.00918, arXiv.org.
    11. Mohammed, Nawaf & Furman, Edward & Su, Jianxi, 2021. "Can a regulatory risk measure induce profit-maximizing risk capital allocations? The case of conditional tail expectation," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 425-436.
    12. Xu, Maochao & Mao, Tiantian, 2013. "Optimal capital allocation based on the Tail Mean–Variance model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 533-543.
    13. Eini, Esmat Jamshidi & Khaloozadeh, Hamid, 2021. "The tail mean–variance optimal portfolio selection under generalized skew-elliptical distribution," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 44-50.
    14. Baishuai Zuo & Chuancun Yin, 2022. "Doubly truncated moment risk measures for elliptical distributions," Papers 2203.01091, arXiv.org.
    15. Owadally, Iqbal & Landsman, Zinoviy, 2013. "A characterization of optimal portfolios under the tail mean–variance criterion," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 213-221.
    16. Ignatieva, Katja & Landsman, Zinoviy, 2015. "Estimating the tails of loss severity via conditional risk measures for the family of symmetric generalised hyperbolic distributions," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 172-186.
    17. Rassoul, Abdelaziz, 2013. "Kernel-type estimator of the conditional tail expectation for a heavy-tailed distribution," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 698-703.
    18. Xiangyu Han & Chuancun Yin, 2022. "Tail Conditional Moments for Location-Scale Mixture of Elliptical Distributions," Mathematics, MDPI, vol. 10(4), pages 1-21, February.
    19. Marri, Fouad & Moutanabbir, Khouzeima, 2022. "Risk aggregation and capital allocation using a new generalized Archimedean copula," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 75-90.
    20. Kim, Joseph H.T. & Kim, So-Yeun, 2019. "Tail risk measures and risk allocation for the class of multivariate normal mean–variance mixture distributions," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 145-157.

    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:jmvana:v:122:y:2013:i:c:p:190-201. 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.