IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v158y2020ics0167715219303220.html
   My bibliography  Save this article

On minimum volume properties of some confidence regions for multiple multivariate normal means

Author

Listed:
  • Bedbur, S.
  • Lennartz, J.M.
  • Kamps, U.

Abstract

In a multi-sample model of multivariate normal distributions with covariance matrices being known or known except for unknown multipliers, simultaneous confidence regions for the mean vectors are provided with minimum volume properties. The univariate case with unknown variances is included.

Suggested Citation

  • Bedbur, S. & Lennartz, J.M. & Kamps, U., 2020. "On minimum volume properties of some confidence regions for multiple multivariate normal means," Statistics & Probability Letters, Elsevier, vol. 158(C).
    • Handle: RePEc:eee:stapro:v:158:y:2020:i:c:s0167715219303220
    DOI: 10.1016/j.spl.2019.108676
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715219303220
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2019.108676?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. Nobuo Shinozaki, 1989. "Improved confidence sets for the mean of a multivariate normal distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(2), pages 331-346, June.
    2. Bradley Efron, 2006. "Minimum volume confidence regions for a multivariate normal mean vector," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(4), pages 655-670, September.
    3. Jeyaratnam, S., 1985. "Minimum volume confidence regions," Statistics & Probability Letters, Elsevier, vol. 3(6), pages 307-308, October.
    4. Richard Samworth, 2005. "Small confidence sets for the mean of a spherically symmetric distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 343-361, June.
    5. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549.
    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. J. T. Gene Hwang & Jing Qiu & Zhigen Zhao, 2009. "Empirical Bayes confidence intervals shrinking both means and variances," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 265-285, January.
    2. Catania, Leopoldo & Proietti, Tommaso, 2020. "Forecasting volatility with time-varying leverage and volatility of volatility effects," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1301-1317.
    3. Jondeau, Eric, 2016. "Asymmetry in tail dependence in equity portfolios," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 351-368.
    4. Punzo, Antonio & Bagnato, Luca, 2022. "Dimension-wise scaled normal mixtures with application to finance and biometry," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    5. Baltagi, Badi H. & Bresson, Georges & Chaturvedi, Anoop & Lacroix, Guy, 2022. "Robust Dynamic Space-Time Panel Data Models Using ?-Contamination: An Application to Crop Yields and Climate Change," IZA Discussion Papers 15815, Institute of Labor Economics (IZA).
    6. Paolella, Marc S. & Polak, Paweł, 2015. "ALRIGHT: Asymmetric LaRge-scale (I)GARCH with Hetero-Tails," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 282-297.
    7. Arismendi, J.C., 2013. "Multivariate truncated moments," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 41-75.
    8. Balakrishnan, N. & Hashorva, E., 2011. "On Pearson-Kotz Dirichlet distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 948-957, May.
    9. Nason, Guy P., 2006. "On the sum of t and Gaussian random variables," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1280-1286, July.
    10. Torri, Gabriele & Giacometti, Rosella & Tichý, Tomáš, 2021. "Network tail risk estimation in the European banking system," Journal of Economic Dynamics and Control, Elsevier, vol. 127(C).
    11. Ñíguez, Trino-Manuel & Perote, Javier, 2016. "Multivariate moments expansion density: Application of the dynamic equicorrelation model," Journal of Banking & Finance, Elsevier, vol. 72(S), pages 216-232.
    12. Koliai, Lyes, 2016. "Extreme risk modeling: An EVT–pair-copulas approach for financial stress tests," Journal of Banking & Finance, Elsevier, vol. 70(C), pages 1-22.
    13. Singh, Vikas Vikram & Lisser, Abdel & Arora, Monika, 2021. "An equivalent mathematical program for games with random constraints," Statistics & Probability Letters, Elsevier, vol. 174(C).
    14. 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.
    15. Brechmann, Eike C. & Hendrich, Katharina & Czado, Claudia, 2013. "Conditional copula simulation for systemic risk stress testing," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 722-732.
    16. Arellano-Valle, Reinaldo B. & Azzalini, Adelchi, 2021. "A formulation for continuous mixtures of multivariate normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    17. Galimberti, Giuliano & Soffritti, Gabriele, 2014. "A multivariate linear regression analysis using finite mixtures of t distributions," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 138-150.
    18. V. Maume-Deschamps & D. Rullière & A. Usseglio-Carleve, 2018. "Spatial Expectile Predictions for Elliptical Random Fields," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 643-671, June.
    19. Toan Luu Duc Huynh, 2019. "Spillover Risks on Cryptocurrency Markets: A Look from VAR-SVAR Granger Causality and Student’s-t Copulas," JRFM, MDPI, vol. 12(2), pages 1-19, April.
    20. Valdez, Emiliano A. & Dhaene, Jan & Maj, Mateusz & Vanduffel, Steven, 2009. "Bounds and approximations for sums of dependent log-elliptical random variables," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 385-397, June.

    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:158:y:2020:i:c:s0167715219303220. 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.