Browse > Article
http://dx.doi.org/10.5351/CKSS.2012.19.6.809

Negative Binomial Varying Coefficient Partially Linear Models  

Kim, Young-Ju (Department of Statistics, Kangwon National University)
Publication Information
Communications for Statistical Applications and Methods / v.19, no.6, 2012 , pp. 809-817 More about this Journal
Abstract
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.
Keywords
Negative binomial; penalized likelihood; semiparametric; smoothing parameter; smoothing spline; varying coefficients;
Citations & Related Records
연도 인용수 순위
  • Reference
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.   DOI   ScienceOn
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.   DOI   ScienceOn
4 Fan, J. and Zhang,W. (1999). Statistical estimation in varying coefficient models, The Annals of Statistics, 27, 1491-1518.   DOI
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.   DOI   ScienceOn
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.   DOI   ScienceOn
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.   DOI   ScienceOn
10 Lu, Y. (2008). Generalized partially linear varying-coefficient models, Journal of Statistical Planning and Inference, 138, 901-914.   DOI   ScienceOn
11 Senturk, D. and Muller, H.-G. (2008). Generalized varying coefficient models for longitudinal data, Biometricka, 95, 653-666.   DOI   ScienceOn
12 Thurston, S. W., Wand, M. P. and Wiencke, J. K. (2000). Negative binomial additive models, Biometrics, 56, 139-144.   DOI   ScienceOn
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.   DOI
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.   DOI   ScienceOn
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.   DOI   ScienceOn
16 Xia, Y., Zhang, W. and Tong, H. (2004). Efficient estimation for semivarying-coefficient models, Biometrika, 91, 661-681.   DOI   ScienceOn
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.   DOI   ScienceOn