IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v80y2017i2d10.1007_s00184-016-0598-4.html
   My bibliography  Save this article

One-sided hyperbolic simultaneous confidence bands for multiple and polynomial regression models

Author

Listed:
  • Sanyu Zhou

    (Shanghai University of Finance and Economics)

Abstract

A simultaneous confidence band is a useful statistical tool in a simultaneous inference procedure. In recent years several papers were published that consider various applications of simultaneous confidence bands, see for example Al-Saidy et al. (Biometrika 59:1056–1062, 2003), Liu et al. (J Am Stat Assoc 99:395–403, 2004), Piegorsch et al. (J R Stat Soc 54:245–258, 2005) and Liu et al. (Aust N Z J Stat 55(4):421–434, 2014). In this article, we provide methods for constructing one-sided hyperbolic imultaneous confidence bands for both the multiple regression model over a rectangular region and the polynomial regression model over an interval. These methods use numerical quadrature. Examples are included to illustrate the methods. These approaches can be applied to more general regression models such as fixed-effect or random-effect generalized linear regression models to construct large sample approximate one-sided hyperbolic simultaneous confidence bands.

Suggested Citation

  • Sanyu Zhou, 2017. "One-sided hyperbolic simultaneous confidence bands for multiple and polynomial regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(2), pages 187-200, February.
    • Handle: RePEc:spr:metrik:v:80:y:2017:i:2:d:10.1007_s00184-016-0598-4
    DOI: 10.1007/s00184-016-0598-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-016-0598-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00184-016-0598-4?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. Liu W. & Jamshidian M. & Zhang Y., 2004. "Multiple Comparison of Several Linear Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 395-403, January.
    2. Wei Pan & Walter Piegorsch & R. West, 2003. "Exact one-sided simultaneous confidence bands via Uusipaikka’s method," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(2), pages 243-250, June.
    3. Obaid M. Al-Saidy & Walter W. Piegorsch & R. Webster West & Daniela K. Nitcheva, 2003. "Confidence Bands for Low-Dose Risk Estimation with Quantal Response Data," Biometrics, The International Biometric Society, vol. 59(4), pages 1056-1062, December.
    4. Walter W. Piegorsch & R. Webster West & Wei Pan & Ralph L. Kodell, 2005. "Low dose risk estimation via simultaneous statistical inferences," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 245-258, January.
    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. Sanyu Zhou & Defa Wang & Jingjing Zhu, 2020. "Construction of simultaneous confidence bands for a percentile hyper-plane with predictor variables constrained in an ellipsoidal region," Statistical Papers, Springer, vol. 61(3), pages 1335-1346, June.

    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. Sanyu Zhou & Defa Wang & Jingjing Zhu, 2020. "Construction of simultaneous confidence bands for a percentile hyper-plane with predictor variables constrained in an ellipsoidal region," Statistical Papers, Springer, vol. 61(3), pages 1335-1346, June.
    2. Christopher Withers & Saralees Nadarajah, 2012. "Maximum modulus confidence bands," Statistical Papers, Springer, vol. 53(4), pages 811-819, November.
    3. Liu, W. & Hayter, A.J. & Piegorsch, W.W. & Ah-Kine, P., 2009. "Comparison of hyperbolic and constant width simultaneous confidence bands in multiple linear regression under MVCS criterion," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1432-1439, August.
    4. Walter W. Piegorsch, 2010. "Translational benchmark risk analysis," Journal of Risk Research, Taylor & Francis Journals, vol. 13(5), pages 653-667, July.
    5. W. Liu & F. Bretz & A. J. Hayter & H. P. Wynn, 2009. "Assessing Nonsuperiority, Noninferiority, or Equivalence When Comparing Two Regression Models Over a Restricted Covariate Region," Biometrics, The International Biometric Society, vol. 65(4), pages 1279-1287, December.
    6. Jamshidian, Mortaza & Liu, Wei & Bretz, Frank, 2010. "Simultaneous confidence bands for all contrasts of three or more simple linear regression models over an interval," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1475-1483, June.
    7. Su, Haiyan & Liang, Hua, 2010. "An empirical likelihood-based method for comparison of treatment effects--Test of equality of coefficients in linear models," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1079-1088, April.
    8. Lu, Xiaolei & Kuriki, Satoshi, 2017. "Simultaneous confidence bands for contrasts between several nonlinear regression curves," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 83-104.
    9. Walter W. Piegorsch & R. Webster West, 2005. "Benchmark Analysis: Shopping with Proper Confidence," Risk Analysis, John Wiley & Sons, vol. 25(4), pages 913-920, August.
    10. Dette, Holger & Pepelyshev, Andrey & Wong, Weng Kee, 2008. "Optimal designs for dose finding experiments in toxicity studies," Technical Reports 2008,09, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    11. Daniela K. Nitcheva & Walter W. Piegorsch & R. Webster West & Ralph L. Kodell, 2005. "Multiplicity-Adjusted Inferences in Risk Assessment: Benchmark Analysis with Quantal Response Data," Biometrics, The International Biometric Society, vol. 61(1), pages 277-286, March.
    12. Signe M. Jensen & Felix M. Kluxen & Christian Ritz, 2019. "A Review of Recent Advances in Benchmark Dose Methodology," Risk Analysis, John Wiley & Sons, vol. 39(10), pages 2295-2315, October.
    13. Jamshidian, Mortaza & Jennrich, Robert I. & Liu, Wei, 2007. "A study of partial F tests for multiple linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6269-6284, August.
    14. Sanyu Zhou, 2018. "An exact method for the multiple comparison of several polynomial regression models with applications in dose-response study," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(3), pages 413-429, July.
    15. Frank Schaarschmidt, 2017. "Multiple treatment comparisons in analysis of covariance with interaction," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 609-628, November.
    16. Gupta, Ramesh C. & Wang, Na, 2009. "Estimation of extra risk and benchmark dose in dose–response models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2036-2050.
    17. Sophia Rosen & Ori Davidov, 2017. "Ordered Regressions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 817-842, December.
    18. Jamshidian, Mortaza & Liu, Wei & Zhang, Ying & Jamishidian, Farid, 2005. "Simreg: a Software Including Some New Developments in Multiple Comparison and Simultaneous Confidence Bands for Linear Regression Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i02).
    19. Mitchell J. Small, 2008. "Methods for Assessing Uncertainty in Fundamental Assumptions and Associated Models for Cancer Risk Assessment," Risk Analysis, John Wiley & Sons, vol. 28(5), pages 1289-1308, October.
    20. Lizhen Lin & Walter W. Piegorsch & Rabi Bhattacharya, 2015. "Nonparametric Benchmark Dose Estimation with Continuous Dose-Response Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 713-731, September.

    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:metrik:v:80:y:2017:i:2:d:10.1007_s00184-016-0598-4. 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.