137
Views
155
CrossRef citations to date
0
Altmetric
Original Articles

Computational Experience With Confidence Regions and Confidence Intervals for Nonlinear Least Squares

&
Pages 67-82 | Published online: 23 Mar 2012

REFERENCES

  • Bard , Y. 1974 . Nonlinear Parameter Estimation New York : Academic Press. .
  • Bates , D. M. and Watts , D. G. 1980 . “Relative Curvature Measures of Nonlinearity” . Journal of the Royal Statistical Society, Ser. B , 42 : 1 – 25 .
  • Beale , E. M. L. 1960 . “Confidence Regions in Non-linear Estimation” . Journal of the Royal Statistical Society, Ser. B , 22 : 41 – 76 .
  • Cook , R. D. , Tsai , C. L. and Wei , B. C. 1984 . “Bias in Nonlinear Regression” University of Wisconsin, Mathematics Research Center. . Technical Summary Report 2645
  • Cook , R. D. and Witmer , J. A. 1985 . “A Note on Parameter-Effects Curvature” . Journal of the American Statistical Association , 80 : 872 – 878 .
  • Dennis , J. E. Jr. , Gay , D. M. and Welsch , R. E. 1981 . “Algorithm 573: NL2SOL—An Adaptive Nonlinear Least Squares Algorithm [E4]” . ACM Transactions on Mathematical Software , 7 : 369 – 383 .
  • Donaldson , J. R. 1985 . “Computational Experience With Confidence Regions and Confidence Intervals for Nonlinear Least Squares” University of Colorado, Dept. of Computer Science. . unpublished M.S. thesis
  • Donaldson , J. R. and Tryon , P. V. 1983 . “Nonlinear Least Squares Regression Using STARPAC” Washington , DC : U.S. Government Printing Office. . National Bureau of Standards Technical Note 1068–2
  • Draper , N. R. and Smith , H. 1981 . Applied Regression Analysis, , 2nd ed. New York : John Wiley. .
  • Duncan , G. T. 1978 . “An Empirical Study of Jackknife-Constructed Confidence Regions in Nonlinear Regression” . Technometrics , 20 : 123 – 129 .
  • Efron , B. 1982 . “The Jackknife, the Bootstrap, and Other Resampling Plans” Philadelphia : Society for Industrial and Applied Mathematics. . Monograph 38 (CBMS-NSF)
  • Efron , B. and Gong , G. 1983 . “A Leisurely Look at the Bootstrap, the Jackknife, and Cross-Validation” . The American Statistician , 27 : 36 – 48 .
  • Gallant , A. R. 1976 . “Confidence Regions for the Parameters of a Nonlinear Regression Model” North Carolina State University, Institute of Statistics. . Mimeograph Series No. 1077
  • Guttman , I. and Meeter , D. A. 1965 . “On Beale's Measures of Non-linearity” . Technometrics , 7 : 623 – 637 .
  • Halperin , M. 1963 . “Confidence Interval Estimation in Non-linear Regression” . Journal of the Royal Statistical Society, Ser. B , 25 : 330 – 333 .
  • Himmelblau , D. M. 1970 . Process Analysis by Statistical Methods New York : John Wiley. .
  • Jennrich , R. I. 1969 . “Asymptotic Properties of Non-linear Least Squares Estimators” . Annals of Mathematical Statistics , 40 : 633 – 643 .
  • Kass , R. E. 1984 . “Canonical Parameterizations and Zero Parameter-effects Curvature” . Journal of the Royal Statistical Society, Ser. B , 46 : 86 – 92 .
  • Marsaglia , G. and Tsang , W. W. 1984 . “A Fast, Easily Implemented Method for Sampling From Decreasing or Symmetric Unimodal Density Functions” . SIAM Journal on Scientific and Statistical Computing , 5 : 349 – 359 .
  • Ratkowsky , D. A. 1983 . Nonlinear Regression Modeling New York : Marcel Dekker. .
  • Schnabel , R. B. 1982 . “Finite Difference Derivatives—Theory and Practice” University of Colorado, Dept. of Computer Science. . internal report
  • Stewart , G. W. 1973 . Introduction to Matrix Computations New York : Academic Press. .

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.