205
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Semiparametric Negative Binomial Regression Models

Pages 475-486 | Received 18 Jul 2009, Accepted 11 Nov 2009, Published online: 19 Feb 2010

References

  • Breslow , N. ( 1984 ). Extra-Poisson variation in log-linear models . Applied Statistics 33 : 38 – 44 .
  • Cameron , A. C. , Trivedi , P. K. ( 1998 ). Regression Analysis of Count Data . New York : Cambridge University Press .
  • Cox , D. R. ( 1983 ). Some remarks on over-dispersion . Biometrika 70 : 269 – 274 .
  • Curry , H. B. , Schoenberg , I. J. ( 1966 ). On Pólya frequency functions IV: The fundamental splines and their limits . Journal of Analyse Mathematique 17 : 71 – 107 .
  • de Boor , C. ( 2001 ). A Practical Guide to Splines. , Revised ed. Applied Mathematical Sciences, 27 . New York : Spring-Verlag .
  • Eilers , P. H. C. , Marx , B. D. ( 1996 ). Flexible smoothing with B-splines and penalties . Statistics in Science 11 : 89 – 121 .
  • Engel , J. ( 1984 ). Models for response data showing extra-Poisson variation . Statistical Neerlandica 38 : 159 – 167 .
  • Fan , J. , Heckman , N. E. , Wand , M. P. ( 1995 ). Local polynomial regression for generalized linear models and quasi-likelihood functions . Journal of the American Statistical Association 90 : 141 – 150 .
  • Frome , E. L. ( 1983 ). The analysis of rates using Poisson regression models . Biometrics 39 : 665 – 674 .
  • Frome , E. L. , Kutner , M. H. , Beauchamp , J. J. ( 1973 ). Regression analysis of Poisson-distributed data . Journal of the American Statistical Association 68 : 935 – 940 .
  • Green , P. J. , Silverman , B. W. ( 1994 ). Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach . London : Chapman and Hall .
  • Green , P. J. , Yandell , B. S. ( 1985 ). Semi-Parametric Generalized Linear Models . Lecture Notes in Statistics, 32 . Berlin : Springer , pp. 44 – 55 .
  • Greenwood , M. , Yule , G. U. (1920). An inquiry into the nature of frequency distributions representative of multiple happenings with particular reference to the occurrence of multiple attacks of disease or of repeated accidents. Journal of the Royal Statistical Society, Series A 83:255–279.
  • Gu , C. ( 2002 ). Smoothing Spline ANOVA Models . New York : Springer-Verlag .
  • Hastie , T. J. , Tibshirani , R. J. ( 1990 ). Generalized Additive Models . New York : Chapman and Hall .
  • Hilbe , J. M. ( 2007 ). Negative Binomial Regression . New York : Cambridge University Press .
  • Kauermann , G. , Tutz , G. ( 2001 ). Testing generalized linear and semiparametric models against smooth alternatives . Journal of the Royal Statistical Society, Series B 63 : 147 – 166 .
  • Lawless , J. F. ( 1987 ). Negative binomial and mixed Poisson regression . The Canadian Journal of Statistics 15 : 209 – 225 .
  • Lindstrom , M. ( 1999 ). Penalized estimation of free-knot splines . Journal of Computational and Graphical Statistics 8 : 333 – 352 .
  • McCullagh , P. , Nelder , J. A. ( 1989 ). Generalized Linear Models . New York : Chapman & Hall .
  • Paul , S. R. , Plackett , R. L. ( 1978 ). Inference sensitivity for Poisson mixtures . Biometrika 65 : 591 – 602 .
  • Ruppert , D. ( 2002 ). Selecting the number of knots for penalized splines . Journal of Computational and Graphical Statistics 11 : 735 – 757 .
  • Ruppert , D. , Wand , M. P. , Carroll , R. J. ( 2003 ). Semiparametric Regression . New York : Cambridge University Press .
  • Schoenberg , I. J. ( 1946 ). Contributions to the problem of approximation of equidistant data by analytic functions . Quarterly Applied Mathematics 4 : 45 – 99 , 112 – 141 .
  • Severini , T. A. , Staniswalis , J. G. ( 1994 ). Quasi-likelihood estimation in semiparametric models . Journal of the American Statistical Association 89 : 501 – 511 .
  • Smith , P. L. ( 1979 ). Splines as a useful and convenient statistical tool . American Statistics 33 : 57 – 62 .
  • Thurston , S. W. , Wand , M. P. , Wiencke , J. K. ( 2000 ). Negative binomial additive models . Biometrics 6 : 139 – 144 .
  • Wold , S. ( 1974 ). Spline functions in data analysis . Technometrics 16 : 1 – 11 .

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.