IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v26y1999i8p933-947.html
   My bibliography  Save this article

Graphical technique for comparing designs for random models

Author

Listed:
  • Juneyoung Lee
  • Andre Khuri

Abstract

Methods for comparing designs for a random (or mixed) linear model have focused primarily on criteria based on single-valued functions. In general, these functions are difficult to use, because of their complex forms, in addition to their dependence on the model's unknown variance components. In this paper, a graphical approach is presented for comparing designs for random models. The one-way model is used for illustration. The proposed approach is based on using quantiles of an estimator of a function of the variance components. The dependence of these quantiles on the true values of the variance components is depicted by plotting the so-called quantile dispersion graphs (QDGs), which provide a comprehensive picture of the quality of estimation obtained with a given design. The QDGs can therefore be used to compare several candidate designs. Two methods of estimation of variance components are considered, namely analysis of variance and maximum-likelihood estimation.

Suggested Citation

  • Juneyoung Lee & Andre Khuri, 1999. "Graphical technique for comparing designs for random models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(8), pages 933-947.
    • Handle: RePEc:taf:japsta:v:26:y:1999:i:8:p:933-947
    DOI: 10.1080/02664769921945
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/02664769921945
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664769921945?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. Robert B. Davies, 1980. "The Distribution of a Linear Combination of χ2 Random Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(3), pages 323-333, November.
    2. Giovagnoli, Alessandra & Sebastiani, Paola, 1989. "Experimental designs for mean and variance estimation in variance components models," Computational Statistics & Data Analysis, Elsevier, vol. 8(1), pages 21-28, May.
    3. A. I. Khuri, 1997. "Quantile dispersion graphs for analysis of variance estimates of variance components," Journal of Applied Statistics, Taylor & Francis Journals, vol. 24(6), pages 711-722.
    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. Loeza-Serrano, S. & Donev, A.N., 2014. "Construction of experimental designs for estimating variance components," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1168-1177.
    2. Escanciano, Juan Carlos & Jacho-Chávez, David T., 2010. "Approximating the critical values of Cramér-von Mises tests in general parametric conditional specifications," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 625-636, March.
    3. Nicolas Städler & Sach Mukherjee, 2017. "Two-sample testing in high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 225-246, January.
    4. Mahmood Kharrati-Kopaei, 2021. "On the exact distribution of the likelihood ratio test statistic for testing the homogeneity of the scale parameters of several inverse Gaussian distributions," Computational Statistics, Springer, vol. 36(2), pages 1123-1138, June.
    5. Elodie Persyn & Richard Redon & Lise Bellanger & Christian Dina, 2018. "The impact of a fine-scale population stratification on rare variant association test results," PLOS ONE, Public Library of Science, vol. 13(12), pages 1-17, December.
    6. A. Basu & A. Mandal & N. Martin & L. Pardo, 2018. "Testing Composite Hypothesis Based on the Density Power Divergence," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 222-262, November.
    7. Liu, Huan & Tang, Yongqiang & Zhang, Hao Helen, 2009. "A new chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 853-856, February.
    8. Yunxuan Jiang & Karen N. Conneely & Michael P. Epstein, 2018. "Robust Rare-Variant Association Tests for Quantitative Traits in General Pedigrees," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(3), pages 491-505, December.
    9. Andrea Cerasa, 2016. "Combining homogeneous groups of preclassified observations with application to international trade," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(3), pages 229-259, August.
    10. Emily Kistner & Keith Muller, 2004. "Exact distributions of intraclass correlation and Cronbach's alpha with Gaussian data and general covariance," Psychometrika, Springer;The Psychometric Society, vol. 69(3), pages 459-474, September.
    11. Aman Ullah & Yong Bao & Yun Wang, 2014. "Exact Distribution of the Mean Reversion Estimator in the Ornstein-Uhlenbeck Process," Working Papers 201413, University of California at Riverside, Department of Economics.
    12. Kulkarni, Pandurang M. & Shah, Arvind K., 1995. "Testing the equality of several binomial proportions to a prespecified standard," Statistics & Probability Letters, Elsevier, vol. 25(3), pages 213-219, November.
    13. Pötscher, Benedikt M. & Preinerstorfer, David, 2021. "Valid Heteroskedasticity Robust Testing," MPRA Paper 117855, University Library of Munich, Germany, revised Jul 2023.
    14. Mohamed Doukali & Xiaojun Song & Abderrahim Taamouti, 2024. "Value‐at‐Risk under Measurement Error," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 86(3), pages 690-713, June.
    15. Chen, Yin-Hsiu & Mukherjee, Bhramar, 2017. "A new variance component score test for testing distributed lag functions with applications in time series analysis," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 122-127.
    16. Hong Zhang & Zheyang Wu, 2023. "The generalized Fisher's combination and accurate p‐value calculation under dependence," Biometrics, The International Biometric Society, vol. 79(2), pages 1159-1172, June.
    17. Dufour, Jean-Marie, 2008. "Exact optimal and adaptive inference in regression models under heteroskedasticity and non-normality of unknown forms," UC3M Working papers. Economics we086027, Universidad Carlos III de Madrid. Departamento de Economía.
    18. El-Bassiouni, M. Y. & Charif, H. A., 2004. "Testing a null variance ratio in mixed models with zero degrees of freedom for error," Computational Statistics & Data Analysis, Elsevier, vol. 46(4), pages 707-719, July.
    19. Peng, Qidi & Schellhorn, Henry, 2018. "On the distribution of extended CIR model," Statistics & Probability Letters, Elsevier, vol. 142(C), pages 23-29.
    20. Shively, Philip A., 2002. "An exact invariant variance ratio test," Economics Letters, Elsevier, vol. 75(3), pages 347-353, May.

    More about this item

    Statistics

    Access and download statistics

    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:taf:japsta:v:26:y:1999:i:8:p:933-947. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.