IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v134y2015icp50-60.html
   My bibliography  Save this article

Central tolerance regions and reference regions for multivariate normal populations

Author

Listed:
  • Dong, Xiaoyu
  • Mathew, Thomas

Abstract

Reference intervals and regions are widely used to identify the measurement range expected from a reference population. Such regions capture the central part of the population, and have potential applications in the field of laboratory medicine. Furthermore, the uncertainty in an estimated reference region can be assessed using a central tolerance region, namely, a region that will contain the population reference region, with a specified confidence level. The construction of a central tolerance region is investigated in this article for a multivariate normal population, and also for a multivariate normal linear regression model. A theoretical framework is developed that will facilitate the numerical computation of the tolerance factor. The performance of a prediction region is also evaluated, in terms of capturing the central part of the population, and the prediction region is found to be unsatisfactory. Some examples from laboratory medicine are used to illustrate the results.

Suggested Citation

  • Dong, Xiaoyu & Mathew, Thomas, 2015. "Central tolerance regions and reference regions for multivariate normal populations," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 50-60.
    • Handle: RePEc:eee:jmvana:v:134:y:2015:i:c:p:50-60
    DOI: 10.1016/j.jmva.2014.10.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X1400236X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2014.10.009?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. Kibria, B. M. Golam & Haq, M. Safiul, 1999. "Predictive Inference for the Elliptical Linear Model," Journal of Multivariate Analysis, Elsevier, vol. 68(2), pages 235-249, February.
    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.
    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. Daniel Garcia-Vicuña & Laida Esparza & Fermin Mallor, 2022. "Hospital preparedness during epidemics using simulation: the case of COVID-19," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(1), pages 213-249, March.

    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. Anwar Joarder, 2008. "Some useful integrals and their applications in correlation analysis," Statistical Papers, Springer, vol. 49(2), pages 211-224, April.
    3. Kozubowski, Tomasz J. & Mazur, Stepan & Podgorski, Krysztof, 2022. "Matrix Variate Generalized Laplace Distributions," Working Papers 2022:7, Örebro University, School of Business.
    4. 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.
    5. Wagner J. F. Silva & Renata M. C. R. Souza & F. J. A. Cysneiros, 2022. "Bivariate elliptical regression for modeling interval-valued data," Computational Statistics, Springer, vol. 37(4), pages 2003-2028, September.
    6. 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.

    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:134:y:2015:i:c:p:50-60. 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.