DOI QR코드

DOI QR Code

Negative Binomial Varying Coefficient Partially Linear Models

  • Kim, Young-Ju (Department of Statistics, Kangwon National University)
  • 투고 : 2012.09.13
  • 심사 : 2012.10.29
  • 발행 : 2012.11.30

초록

We propose a semiparametric inference for a generalized varying coefficient partially linear model(VCPLM) for negative binomial data. The VCPLM is useful to model real data in that varying coefficients are a special type of interaction between explanatory variables and partially linear models fit both parametric and nonparametric terms. The negative binomial distribution often arise in modelling count data which usually are overdispersed. The varying coefficient function estimators and regression parameters in generalized VCPLM are obtained by formulating a penalized likelihood through smoothing splines for negative binomial data when the shape parameter is known. The performance of the proposed method is then evaluated by simulations.

키워드

참고문헌

  1. Ahmad, I., Leelahanon, S. and Li, Q. (2010). Efficient estimation of a semiparametric partially linear varying coefficient model, The Annals of Statistics, 33, 258-283.
  2. Fan, J. and Huang, T. (2005). Profile likelihood inference on semiparametric varying-coefficient partially linear models, Bernoulli, 11, 1031-1057. https://doi.org/10.3150/bj/1137421639
  3. Fan, J., Yao, Q. and Cai, Z. (2003). Adaptive varying-coefficient linear models, Journal of the Royal Statistical Society Series B, 65, 57-80. https://doi.org/10.1111/1467-9868.00372
  4. Fan, J. and Zhang,W. (1999). Statistical estimation in varying coefficient models, The Annals of Statistics, 27, 1491-1518. https://doi.org/10.1214/aos/1017939139
  5. Gu, C. (2002). Smoothing Spline ANOVA Models, Springer-Verlag.
  6. Gu, C. and Kim, Y.-J. (2002). Penalized likelihood regression: General formulation and efficient approximation, Canadian Journal of Statistics, 30, 619-628. https://doi.org/10.2307/3316100
  7. Gu, C. and Xiang, D. (2001). Cross-validating non-Gaussian data: Generalized approximate crossvalidation revisited, Journal of Computational and Graphical Statistics, 10, 581-591. https://doi.org/10.1198/106186001317114992
  8. Hastie, T. and Tibshirani, R. (1993). Varying-coefficient models, Journal of the Royal Statistical Society Series B, 55, 757-796.
  9. Kim, Y.-J. and Gu, C. (2004). Smoothing spline Gaussian regression: More scalable computation via efficient approximation, Journal of the Royal Statistical Society Series B, 66, 337-356. https://doi.org/10.1046/j.1369-7412.2003.05316.x
  10. Lu, Y. (2008). Generalized partially linear varying-coefficient models, Journal of Statistical Planning and Inference, 138, 901-914. https://doi.org/10.1016/j.jspi.2007.02.010
  11. Senturk, D. and Muller, H.-G. (2008). Generalized varying coefficient models for longitudinal data, Biometricka, 95, 653-666. https://doi.org/10.1093/biomet/asn006
  12. Thurston, S. W., Wand, M. P. and Wiencke, J. K. (2000). Negative binomial additive models, Biometrics, 56, 139-144. https://doi.org/10.1111/j.0006-341X.2000.00139.x
  13. Wahba, G. (1985). A comparison of GCV and GML for choosing the smoothing parameter in the generalized spline smoothing problem, The Annals of Statistics, 13, 1378-1402. https://doi.org/10.1214/aos/1176349743
  14. Wood, S. N. (2008). Fast stable direct fitting and smoothness selection for generalized additive models, Journal of the Royal Statistical Society Series B, 70, 495-518. https://doi.org/10.1111/j.1467-9868.2007.00646.x
  15. Wood, S. N. (2011). Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models, Journal of the Royal Statistical Society Series B, 73, 3-36. https://doi.org/10.1111/j.1467-9868.2010.00749.x
  16. Xia, Y., Zhang, W. and Tong, H. (2004). Efficient estimation for semivarying-coefficient models, Biometrika, 91, 661-681. https://doi.org/10.1093/biomet/91.3.661
  17. Xiang, D. and Wahba, G. (1996). A generalized approximate cross validation for smoothing splines with non-Gaussian data, Statistica Sinica, 6, 675-692.
  18. Zhang, W., Lee, S. and Song, X. (2002). Local polynomial fitting semivarying coefficient model, Journal of Multivariate Analysis, 82, 166-188. https://doi.org/10.1006/jmva.2001.2012