20
Views
23
CrossRef citations to date
0
Altmetric
Original Articles

An Empirical Study of Jackknife-Constructed Confidence Regions in Nonlinear Regression

Pages 123-129 | Published online: 09 Apr 2012

REFERENCES

  • Arvesen , J. N. and Salsburg , D. S. 1973 . “ Approximate tests and confidence intervals using the jackknife. ” . In Perspectives in Biometrics Edited by: Elashoff , R. M. New York : Academic Press. .
  • Beale , E. M. L. 1960 . Confidence regions in nonlinear estimation . J. Roy. Statist. Soc., B , 22 : 41 – 76 .
  • Box , G. E. P. and Draper , N. R. 1965 . The Bayesian estimation of common parameters from several responses . Biometrika , 52 : 355 – 365 .
  • Box , G. E. P. and Hunter , W. G. 1965 . The experimental study of physical mechanisms . Technometrics , 4 : 301 – 318 .
  • Bradley , R. A. and Gart , J. J. 1962 . The asymptotic properties of ML estimators when sampling from associated populations . Biometrika , 49 : 205 – 214 .
  • Brillinger , D. R. 1964 . The asymptotic behavior of Tukey's general method of setting approximate confidence limits (the jackknife) when applied to maximum likelihood estimates . Rev. Inst. Int. Statist. , 32 : 202 – 206 .
  • Chambers , J. M. 1973 . Fitting nonlinear models: numerical techniques . Biometrika , 60 : 1 – 14 .
  • Cook , R. D. 1975 . Detection of influential observations in linear regression School of Statistics, U. of Minnesota. . Tech. Report No. 256
  • Draper , N. R. and Shaw , D. E. 1974 . The effects of nonlinearity in regression models Madison : U. of Wisconsin. . Part 1: A procedure for examination of the adequacy of the linear approximation. Mathematics Research Center Tech. Report No. 1408
  • Draper , N. R. and Smith , H. 1966 . Applied Regression Analysis. New York : John Wiley and Sons, Inc. .
  • Duncan , G. T. and Layard , M. W. J. 1973 . A Monte Carlo study of asymptotically robust tests for correlation . Biometrika , 60 : 551 – 558 .
  • Gallant , A. R. 1975 . Nonlinear regression . The American Statistician , 29 : 73 – 81 .
  • Gallant , A. R. 1975 . Testing a subset of the parameters of a nonlinear regression model . J. Amer. Statist. Assoc. , 70 : 927 – 932 .
  • Guttman , I. and Meeter , D. A. 1965 . On Beale's measures of nonlinearity . Technometrics , 7 : 623 – 637 .
  • Halperin , M. 1963 . Confidence interval estimation in nonlinear regression . J. Roy. Statist. Soc., B , 25 : 330 – 333 .
  • Hartley , H. O. 1964 . Exact confidence regions for the parameters in nonlinear regression laws . Biometrika , 51 : 347 – 353 .
  • Hinkley , D. V. 1977 . Jackknife confidence limits using student-t approximations . Biometrika , 64 : 21 – 28 .
  • Hinkley , D. V. 1976 . On jackknifing in unbalanced situations Division of Biostatistics, Stanford University. . Tech. Report No. 22
  • Jennrich , R. I. 1969 . Asymptotic properties of nonlinear least squares estimators . Ann. Math. Statist. , 40 : 633 – 643 .
  • Kanemasu , H. 1972 . Topics in model building. Part I. Introduction and review of past work Madison : Dept. of Statistics, U. of Wisconsin. . Technical Report No. 320
  • Kinderman , A. J. and Ramage , J. G. 1976 . Computer generation of normal random variables . J. Amer. Statist. Assoc. , 71 : 893 – 896 .
  • Kish , L. and Frankel , M. R. 1974 . Inference from complex samples (with discussion) . J. Roy. Statist. Soc., B. , 36 : 1 – 37 .
  • Knuth , D. E. 1969 . The Art of Computer Programming Vol. 2 , Reading , MA : Addison-Wesley. .
  • Marquardt , D. W. 1963 . An algorithm for least squares estimation of nonlinear parameters . S.I.A.M.J. Appl. Math. , 11 : 431 – 441 .
  • Miller , R. G. 1974 . An unbalanced jackknife . Annals of Statistics , 2 : 880 – 891 .
  • Miller , R. G. 1974 . The jackknife—a review . Biometrika , 61 ( No. 1 ) : 1 – 15 .
  • Mosteller , F. and Tukey , J. W. 1964 . “ Data analysis, including statistics. ” . In Handbook of Social Psychology Edited by: Lindzey , O. and Aronson , E. Vol. 2 , Reading , MA : Addison-Wesley. .
  • Rao , J. N. K. and Webster , J. 1966 . On two methods of bias reduction in the estimation of ratios . Biometrika , 53 : 571 – 577 .
  • Tarone , R. E. 1974 . Asymptotic properties of maximum likelihood estimators in the general sampling framework, and some results in non-normal linear regression , Ph.D. thesis Davis : Dept. of Mathematics, U. of California. .
  • Tukey , J. W. 1958 . Bias and confidence in not-quite large samples (Abstract) . Ann. Math. Statist. , 29 : 614
  • Williams , E. J. 1962 . Exact fiducial limits in nonlinear estimation . J. Roy. Statist. Soc., B , 24 : 125 – 139 .

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.