94
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Comparison of simultaneous confidence bands for univariate polynomial regression over an interval

Pages 589-596 | Received 23 Apr 2013, Accepted 06 Aug 2013, Published online: 25 Jan 2016

References

  • Johansen, S., Johnstone, I. (1990). Hotelling’s theorem on the volume of tubes: some illustrations in simultaneous inference and data analysis. Ann. Stat. 18: 652–684.
  • Johnstone, I., Siegmund, D. (1989). On Hotelling’s formula for the volume of tubes and Naiman’s inequality. Ann. Stat. 17: 184–194.
  • Knowles, M., Siegmund, D. (1989). On Hotelling’s approach to testing for a nonlinear parameter in regression. Int. Stat. Rev. 57: 205–220.
  • Kosorok, M.R., Qu, R. (1999). Exact simultaneous confidence bands for a collection of univariate polynomials in regression analysis. Stat. Med. 18: 613–620.
  • Liu, W., Jamshidian, M., Zhang, Y., Donnelly, J. (2005). Simulation-based simultaneous confidence bands for a multiple linear regression model when the covariates are constrained. J. Comput. Graph. Stat. 14: 459–484.
  • Liu, W., Wynn, H.P., Hayter, A.J. (2008). Statistical inferences for linear regression models when the covariates have functional relationships: polynomial regression. J. Stat. Comput. Simul. 78: 315–324.
  • Naiman, D.Q. (1986). Conservative confidence bands in curvilinear regression. Ann. Stat. 14: 896–906.
  • Scheffé, H. (1953). A method for judging all contrasts in analysis of variance. Biometrika 40: 87–104.
  • Selvin, S. (1998). Modern Applied Biostatistical Methods using S-plus. Oxford: Oxford University Press.
  • Spurrier, J.D. (1993). Comparison of simultaneous confidence bands for quadratic regression over a finite interval. Technometrics 35: 315–320.
  • Sun, J., Loader, C.R. (1994). Simultaneous confidence bands for linear regression and smoothing. Ann. Stat. 22: 1328–1346.
  • Working, H., Hotelling, H. (1929). Applications of the theory of error to the interpretation of trends. J. Am. Stat. Assoc. 24: 73–85.
  • Wynn, H.P. (1984). An exact confidence band for one-dimensional polynomial regression. Biometrika 71: 375–379.
  • Wynn, H.P., Bloomfield, P. (1971). Simultaneous confidence bands in regression analysis. J. Royal Stat. Soc. (B) 33: 202–1217.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.