IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v81y2011i11p1635-1647.html
   My bibliography  Save this article

Estimates of low bias for the multivariate normal

Author

Listed:
  • Withers, Christopher S.
  • Nadarajah, Saralees

Abstract

Given a sample from a multivariate normal with mean , a method is given for obtaining estimates with low bias for a function of the parameters. When the function is a product of positive powers of the parameters, an unbiased estimate is available. Estimates of ratios like [mu]1/[mu]2 are given with bias ~n-5, where n is the sample size. Simulation studies show superior performance of these estimates versus traditional ones.

Suggested Citation

  • Withers, Christopher S. & Nadarajah, Saralees, 2011. "Estimates of low bias for the multivariate normal," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1635-1647, November.
  • Handle: RePEc:eee:stapro:v:81:y:2011:i:11:p:1635-1647
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715211002161
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Misra, Neeraj & Singh, Harshinder & Demchuk, Eugene, 2005. "Estimation of the entropy of a multivariate normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 324-342, February.
    2. Zografos, K. & Nadarajah, S., 2005. "Expressions for Rényi and Shannon entropies for multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 71(1), pages 71-84, January.
    3. Sun, Dongchu & Sun, Xiaoqian, 2006. "Estimation of multivariate normal covariance and precision matrices in a star-shape model with missing data," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 698-719, March.
    4. Kollo, T. & Vonrosen, D., 1995. "Minimal Moments and Cumulants of Symmetric Matrices: An Application to the Wishart Distribution," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 149-164, November.
    5. Dongchu Sun & Xiaoqian Sun, 2005. "Estimation of the multivariate normal precision and covariance matrices in a star-shape model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(3), pages 455-484, September.
    6. Hutson, Alan D., 2002. "Quasi-medians are robust and relatively efficient estimators of a common mean given multivariate normality," Statistics & Probability Letters, Elsevier, vol. 57(4), pages 403-408, May.
    7. Yanagihara, Hirokazu, 2006. "Corrected version of AIC for selecting multivariate normal linear regression models in a general nonnormal case," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1070-1089, May.
    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. Carlos A. Medel & Pablo M. Pincheira, 2016. "The out-of-sample performance of an exact median-unbiased estimator for the near-unity AR(1) model," Applied Economics Letters, Taylor & Francis Journals, vol. 23(2), pages 126-131, February.

    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. He, Daojiang & Xu, Kai, 2014. "Estimation of the Cholesky decomposition in a conditional independent normal model with missing data," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 27-39.
    2. Carol Alexander & José María Sarabia, 2012. "Quantile Uncertainty and Value‐at‐Risk Model Risk," Risk Analysis, John Wiley & Sons, vol. 32(8), pages 1293-1308, August.
    3. Mohammed S. Kotb & Huda M. Alomari, 2024. "Estimating the entropy of a Rayleigh model under progressive first-failure censoring," Statistical Papers, Springer, vol. 65(5), pages 3135-3154, July.
    4. Liang, Ye & Sun, Dongchu, 2012. "Objective priors for generative star-shape models," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 991-997.
    5. Xiaoqian Sun & Dongchu Sun, 2007. "Estimation of a Multivariate Normal Covariance Matrix with Staircase Pattern Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(2), pages 211-233, June.
    6. Daya K. Nagar & Saralees Nadarajah & Idika E. Okorie, 2017. "A New Bivariate Distribution with One Marginal Defined on the Unit Interval," Annals of Data Science, Springer, vol. 4(3), pages 405-420, September.
    7. Leonenko, Nikolaj & Seleznjev, Oleg, 2010. "Statistical inference for the [epsilon]-entropy and the quadratic Rényi entropy," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 1981-1994, October.
    8. Nathan Lassance & Frédéric Vrins, 2021. "Minimum Rényi entropy portfolios," Annals of Operations Research, Springer, vol. 299(1), pages 23-46, April.
    9. Gianluca Cubadda & Alain Hecq & Sean Telg, 2019. "Detecting Co‐Movements in Non‐Causal Time Series," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 81(3), pages 697-715, June.
    10. Kayal, Suchandan & Kumar, Somesh, 2013. "Estimation of the Shannon’s entropy of several shifted exponential populations," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1127-1135.
    11. Christopher Withers & Saralees Nadarajah, 2013. "Calibration with low bias," Statistical Papers, Springer, vol. 54(2), pages 371-379, May.
    12. Sun, Dongchu & Sun, Xiaoqian, 2006. "Estimation of multivariate normal covariance and precision matrices in a star-shape model with missing data," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 698-719, March.
    13. Bhattacharya, Bhaskar, 2006. "Maximum entropy characterizations of the multivariate Liouville distributions," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1272-1283, July.
    14. Lakshmi Kanta Patra & Suchandan Kayal & Somesh Kumar, 2020. "Estimating a function of scale parameter of an exponential population with unknown location under general loss function," Statistical Papers, Springer, vol. 61(6), pages 2511-2527, December.
    15. W. V. Félix de Lima & A. D. C. Nascimento & G. J. A. Amaral, 2021. "Entropy-based pivotal statistics for multi-sample problems in planar shape," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 153-178, March.
    16. Yanagihara, Hirokazu & Tonda, Tetsuji & Matsumoto, Chieko, 2006. "Bias correction of cross-validation criterion based on Kullback-Leibler information under a general condition," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 1965-1975, October.
    17. Burkschat Marco & Kamps Udo & Kateri Maria, 2013. "Estimating scale parameters under an order statistics prior," Statistics & Risk Modeling, De Gruyter, vol. 30(3), pages 205-219, August.
    18. Vuong, Q.N. & Bedbur, S. & Kamps, U., 2013. "Distances between models of generalized order statistics," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 24-36.
    19. Nader Ebrahimi & S.N.U.A. Kirmani & Ehsan S. Soofi, 2011. "Predictability of operational processes over finite horizon," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(6), pages 531-545, September.
    20. Cubadda, Gianluca & Guardabascio, Barbara & Hecq, Alain, 2017. "A vector heterogeneous autoregressive index model for realized volatility measures," International Journal of Forecasting, Elsevier, vol. 33(2), pages 337-344.

    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:81:y:2011:i:11:p:1635-1647. 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.