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http://dx.doi.org/10.5351/CKSS.2005.12.3.743

Computation and Smoothing Parameter Selection In Penalized Likelihood Regression  

Kim Young-Ju (Department of Information and Statistics, Kangwon National University)
Publication Information
Communications for Statistical Applications and Methods / v.12, no.3, 2005 , pp. 743-758 More about this Journal
Abstract
This paper consider penalized likelihood regression with data from exponential family. The fast computation method applied to Gaussian data(Kim and Gu, 2004) is extended to non Gaussian data through asymptotically efficient low dimensional approximations and corresponding algorithm is proposed. Also smoothing parameter selection is explored for various exponential families, which extends the existing cross validation method of Xiang and Wahba evaluated only with Bernoulli data.
Keywords
Cross-validation; Kullback-Leibler; Penalized likelihood; Smoothing parameter;
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  • Reference
1 Gu, C. (1990). Adaptive spline smoothing in non Gaussian regression models. Journal of American Statistical Association 85, 801-807   DOI   ScienceOn
2 Gu, C. (1992). Cross-validating non-Gaussian data. Journal of Computational Graphics and Statistics 1, 169-179   DOI   ScienceOn
3 Gu, C. (2002). Smoothing Spline ANOVA Models. New York: Springer-Verlag
4 Gu, C. and Kim, Y.-J. (2002). Penalized likelihood regression: General formulation and efficient approximation. Canadian Journal of Statistics 30, 619-628   DOI   ScienceOn
5 Gu, C. and Qiu, C. (1994). Penalized likelihood regression: A simple asymptotic analysis. Statistical Sinica 4, 297-304
6 Gu, C. and Wang, J. (2003). Penalized likelihood density estimation: Direct cross validation and scalable approximation. Statistical Sinica 13, 811-826
7 Gu, C. and Xiang, D. (2001). Cross-validating non-Gaussian data: Generalized approximate cross-validation revisited. Journal of Computational Graphics and Statistics 10, 581-591   DOI   ScienceOn
8 Kim, Y-J. (2003), Smoothing splines regression: Scalable computation and cross-validation, Ph.D. thesis, Purdue University, West Lafayette, IN, USA
9 Kim, Y-J. and Gu, C. (2004). Smoothing spline Gaussian regression: More scalable computation via efficient approximation. Journal of Royal Statistical Society Series B 66, 337-356   DOI   ScienceOn
10 Wahba, G. (1990). Spline Models for Observational Data, Vol 59 of CBMS-NSF Regional Conference Series in Applied Mathematics, Philadelphia: SIAM
11 Xiang, D. and Wahba, G. (1996). A generalized approximate cross validation for smoothing splines with non-Gaussian data. Statistical Sinica 6, 675-692
12 O' Sullivan, F., Yandell, B., and Raynor, W. (1986). Automatic smoothing of regression functions in generalized linear models. Journal of American Statistical Association 81, 96-103   DOI   ScienceOn
13 Cox, D.D. and O' Sullivan, F. (1990). Asymptotic analysis of penalized likelihood and related estimators. Annuls of Statistics 18, 124-145
14 Green, P. J. and Yandell, B. (1985). Semi-parametric generalized linear models. In R. Gilchrist, B. Francis, and J. Whittaker (Eds.), Proceedings of the GLIMBS Conference, pp. 44-55. Berlin: Springer-Verlag
15 Silverman, B. W. (1978). Density ratios, empirical likelihood and cot death. Applied Statistics 27, 26-33   DOI   ScienceOn