Penalized likelihood regression: General formulation and efficient approximation

Canadian Journal of Statistics

Volumn 30, Issue 4, 2002, Pages 619-628

  Gu, Chong ^a   Kim, Young Ju ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

Censored data; Convergence rate; Exponential family; Likelihood; Regression

Indexed keywords

EID: 0036975172     PISSN: 03195724     EISSN: None     Source Type: Journal    
DOI: 10.2307/3316100     Document Type: Article

References (25)

1. D. D. Cox & F. O'Sullivan (1990). Asymptotic analysis of penalized likelihood and related estimators. The Annals of Statistics, 18, 124-145.
2. T. R. Fleming & D. P. Harrington (1991). Counting Processes and Survival Analysis. Wiley, New York.
3. F. Gao (1999). Penalized Multivariate Logistic Regression with a Large Data Set. Doctoral dissertation, University of Wisconsin-Madison.
4. F. Gao, G. Wahba, R. Klein & B. E. K. Klein (2001). Smoothing spline ANOVA for multivariate Bernoulli observations, with application to ophthalmology data (with discussion). Journal of the American Statistical Association, 96, 127-160.
5. P. J. Green & B. Yandell (1985). Semi-parametric generalized linear models. In Generalized Linear Models: Proceedings of the 2nd Conference on Generalized Linear Models (GLIM 85), held in Lancaster, UK, September 16-19, 1985 (R. Gilchrist, B. Francis & J. Whittaker, eds.), Lecture Notes in Statistics 32, Springer-Verlag, Berlin, pp. 44-55.
6. C. Gu (1990). Adaptive spline smoothing in non Gaussian regression models. Journal of the American Statistical Association, 85, 801-807.
7. C. Gu (1992). Cross-validating non-Gaussian data. Journal of Computational and Graphical Statistics, 1, 169-179.
8. C. Gu (2002). Smoothing Spline ANOVA Models. Springer-Verlag, New York.
9. C. Gu & C. Qiu (1993). Smoothing spline density estimation: theory. The Annals of Statistics, 21, 217-234.
10. C. Gu & C. Qiu (1994). Penalized likelihood regression: a simple asymptotic analysis. Statistica Sinica, 4, 297-304.
11. C. Gu & D. Xiang (2001). Cross-validating non-Gaussian data: generalized approximate cross-validation revisited. Journal of Computational and Graphical Statistics, 10, 581-591.
12. M. F. Hutchinson & P. E. Gessler (1994). Splines - more than just a smooth interpolate. Geoderma, 62, 45-67.
13. Y.-J. Kim & C. Gu (2002). Penalized Least Squares Regression: Fast Computation via Efficient Approximation. Technical report, Department of Statistics, Purdue University, West Lafayette, Indiana.
14. X. Lin, G. Wahba, D. Xiang, F. Gao, R. Klein & B. E. K. Klein (2000). Smoothing spline ANOVA models for large data sets with Bernoulli observations and the randomized GACV. The Annals of Statistics, 28, 1570-1600.
15. Z. Luo & G. Wahba (1997). Hybrid adaptive splines. Journal of the American Statistical Association, 92, 107-116.
16. P. McCullagh & J. A. Neider (1989). Generalized Linear Models (2nd Edition). Chapman & Hall, London.
17. F. O'Sullivan, B. Yandell & W. Raynor (1986). Automatic smoothing of regression functions in generalized linear models. Journal of the American Statistical Association, 81, 96-103.
18. B. W. Silverman (1978). Density ratios, empirical likelihood and cot death. Applied Statistics, 27, 26-33.
19. B. W. Silverman (1982). On the estimation of a probability density function by the maximum penalized likelihood method. The Annals of Statistics, 10, 795-810.
20. F. Utreras (1981). Optimal smoothing of noisy data using spline functions. SIAM Journal on Scientific and Statistical Computing, 2, 349-362.
21. G. Wahba (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.
22. G. Wahba (1990). Spline Models for Observational Data. CBMS-NSF Regional Conference Series in Applied Mathematics 59. SIAM, Philadelphia, PA.
23. H. F. Weinberger (1974). Variational Methods for Eigenvalue Approximation. CBMS-NSF Regional Conference Series in Applied Mathematics 15. SIAM, Philadelphia, PA.
24. S. N. Wood (2000). Modelling and smoothing parameter selection with multiple quadratic penalties. Journal of the Royal Statistical Society Series B, 62, 413-428.
25. D. Xiang & G. Wahba (1996). A generalized approximate cross validation for smoothing splines with non-Gaussian data. Statistica Sinica, 6, 675-692.