IDEAS home Printed from https://ideas.repec.org/a/spr/jstada/v7y2020i1d10.1186_s40488-020-00105-w.html
   My bibliography  Save this article

Exact distributions of statistics for making inferences on mixed models under the default covariance structure

Author

Listed:
  • Samaradasa Weerahandi

    (X-Techniques)

  • Ching-Ray Yu

    (Pfizer)

Abstract

At this juncture when mixed models are heavily employed in applications ranging from clinical research to business analytics, the purpose of this article is to extend the exact distributional result of Wald (Ann. Math. Stat. 18: 586–589, 1947) to handle models involving a number of variance components.Due to the unavailability of exact distributional results for underlying statistics, currently available methods provide small group/sample inference only for balanced ANOVA models or simple regression models. The exact distributional results developed in this article should prove useful in making inferences by such methods as parametric bootstrap, fiducial, and generalized p-value approach, when there are a number of variance components to deal with.

Suggested Citation

  • Samaradasa Weerahandi & Ching-Ray Yu, 2020. "Exact distributions of statistics for making inferences on mixed models under the default covariance structure," Journal of Statistical Distributions and Applications, Springer, vol. 7(1), pages 1-14, December.
    • Handle: RePEc:spr:jstada:v:7:y:2020:i:1:d:10.1186_s40488-020-00105-w
    DOI: 10.1186/s40488-020-00105-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1186/s40488-020-00105-w
    File Function: Abstract
    Download Restriction: no
    File URL: https://libkey.io/10.1186/s40488-020-00105-w?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
    ---><---

    References listed on IDEAS

    as
    1. Gamage, Jinadasa & Mathew, Thomas & Weerahandi, Samaradasa, 2013. "Generalized prediction intervals for BLUPs in mixed models," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 226-233.
    2. Hannig, Jan & Iyer, Hari & Patterson, Paul, 2006. "Fiducial Generalized Confidence Intervals," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 254-269, March.
    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. Roy, Anindya & Bose, Arup, 2009. "Coverage of generalized confidence intervals," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1384-1397, August.
    2. Sam W & Peijin X & Ching RY & Kelly HZ, 2018. "Improved EBLUPs in Mixed-Effects Regression Models," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 4(4), pages 78-86, January.
    3. Li, Xinmin & Wang, Juan & Liang, Hua, 2011. "Comparison of several means: A fiducial based approach," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1993-2002, May.
    4. Russell J. Bowater, 2017. "A defence of subjective fiducial inference," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(2), pages 177-197, April.
    5. Yuliang Yin & Bingbing Wang, 2016. "The Agreement between the Generalized Value and Bayesian Evidence in the One-Sided Testing Problem," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2016, pages 1-7, May.
    6. Mathew, Thomas & Menon, Sandeep & Perevozskaya, Inna & Weerahandi, Samaradasa, 2016. "Improved prediction intervals in heteroscedastic mixed-effects models," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 48-53.
    7. Hannig, Jan & Lai, Randy C.S. & Lee, Thomas C.M., 2014. "Computational issues of generalized fiducial inference," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 849-858.
    8. A. Malekzadeh & M. Kharrati-Kopaei & S. Sadooghi-Alvandi, 2014. "Comparing exponential location parameters with several controls under heteroscedasticity," Computational Statistics, Springer, vol. 29(5), pages 1083-1094, October.
    9. Hsin-I Lee & Hungyen Chen & Hirohisa Kishino & Chen-Tuo Liao, 2016. "A Reference Population-Based Conformance Proportion," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(4), pages 684-697, December.
    10. Weizhong Tian & Yaoting Yang & Tingting Tong, 2022. "Confidence Intervals Based on the Difference of Medians for Independent Log-Normal Distributions," Mathematics, MDPI, vol. 10(16), pages 1-14, August.
    11. Piao Chen & Zhi‐Sheng Ye & Xun Xiao, 2019. "Pairwise model discrimination with applications in lifetime distributions and degradation processes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(8), pages 675-686, December.
    12. CHEN, Piao & YE, Zhi-Sheng, 2018. "A systematic look at the gamma process capability indices," European Journal of Operational Research, Elsevier, vol. 265(2), pages 589-597.
    13. Kharrati-Kopaei, Mahmood & Malekzadeh, Ahad & Sadooghi-Alvandi, Mohammad, 2013. "Simultaneous fiducial generalized confidence intervals for the successive differences of exponential location parameters under heteroscedasticity," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1547-1552.
    14. Philip L.H. Yu & Thomas Mathew & Yuanyuan Zhu, 2017. "A generalized pivotal quantity approach to portfolio selection," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(8), pages 1402-1420, June.
    15. Randy C. S. Lai & Jan Hannig & Thomas C. M. Lee, 2015. "Generalized Fiducial Inference for Ultrahigh-Dimensional Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 760-772, June.
    16. Wang, Bing Xing, 2012. "Generalized interval estimation for the Birnbaum–Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4320-4326.
    17. Theerapong Kaewprasert & Sa-Aat Niwitpong & Suparat Niwitpong, 2022. "Simultaneous Confidence Intervals for the Ratios of the Means of Zero-Inflated Gamma Distributions and Its Application," Mathematics, MDPI, vol. 10(24), pages 1-22, December.
    18. Bebu, Ionut & Luta, George & Mathew, Thomas & Kennedy, Paul A. & Agan, Brian K., 2016. "Parametric cost-effectiveness inference with skewed data," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 210-220.
    19. Xuhua Liu & Xingzhong Xu, 2016. "Confidence distribution inferences in one-way random effects model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 59-74, March.
    20. Wang, Xiaofei & Wang, Bing Xing & Hong, Yili & Jiang, Pei Hua, 2021. "Degradation data analysis based on gamma process with random effects," European Journal of Operational Research, Elsevier, vol. 292(3), pages 1200-1208.

    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:spr:jstada:v:7:y:2020:i:1:d:10.1186_s40488-020-00105-w. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.