Fast Stable Direct Fitting and Smoothness Selection for Generalized Additive Models
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Akaike, 1973, Proc. 2nd Int. Symp Information Theory, 267
Borchers, 1997, Improving the precision of the daily egg production method using generalized additive models, Can. J. Fish. Aquat. Sci., 54, 2727, 10.1139/f97-134
Breslow, 1993, Approximate inference in generalized linear mixed models, J. Am. Statist. Ass., 88, 9
Brezger, 2007, BayesX 1.5.0. University of Munich
Brezger, 2006, Generalized structured additive regression based on Bayesian P-splines, Computnl Statist. Data Anal., 50, 967, 10.1016/j.csda.2004.10.011
Cline, 1979, An estimate for the condition number of a matrix. SIAM J, Numer. Anal., 13, 293, 10.1137/0713027
Craven, 1979, Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross validation, Numer. Math., 31, 377, 10.1007/BF01404567
Dennis, 1983, Numerical Methods for Unconstrained Optimization and Nonlinear Equations
Dongarra, 1978, LINPACK Users Guide
Eilers, 2002, Generalized linear additive smooth structures, J. Computnl Graph. Statist., 11, 758, 10.1198/106186002844
Fahrmeir, 2004, Penalized structured additive regression for space time data: a Bayesian perspective, Statist. Sin., 14, 731
Fahrmeir, 2001, Bayesian inference for generalized additive mixed models based on Markov random field priors, Appl. Statist., 50, 201
Figueiras, 2005, A bootstrap method to avoid the effect of concurvity in generalized additive models in time series studies of air pollution, J. Epidem. Commty Hlth, 59, 881, 10.1136/jech.2004.026740
Gill, 1981, Practical Optimization
Golub, 1996, Matrix Computations
Gu, 1992, Cross validating non-Gaussian data, J. Computnl Graph. Statist., 1, 169
Gu, 2004, General smoothing splines
Gu, 1991, Minimizing GCV/GML scores with multiple smoothing parameters via the Newton method, SIAM J. Scient. Statist. Comput., 12, 383, 10.1137/0912021
Gu, 2001, Cross-validating non-Gaussian data: generalized approximate cross-validation revisited, J. Computnl Graph. Statist., 10, 581, 10.1198/106186001317114992
Hastie, 1986, Generalized additive models (with discussion), Statist. Sci., 1, 297
Hastie, 1990, Generalized Additive Models
Hastie, 1993, Varying-coefficient models, J. R. Statist. Soc. B, 55, 757
Kim, 2004, Smoothing spline Gaussian regression: more scalable computation via efficient approximation, J. R. Statist. Soc. B, 66, 337, 10.1046/j.1369-7412.2003.05316.x
Lin, 1999, Inference in generalized additive mixed models by using smoothing splines, J. R. Statist. Soc. B, 61, 381, 10.1111/1467-9868.00183
Mallows, 1973, Some comments on Cp, Technometrics, 15, 661
Mammen, 2005, Bandwidth selection for smooth backfitting in additive models, Ann. Statist., 33, 1260, 10.1214/009053605000000101
Marx, 1998, Direct generalized additive modeling with penalized likelihood, Computnl Statist. Data Anal., 28, 193, 10.1016/S0167-9473(98)00033-4
O'Sullivan, 1986, A statistical perspective on ill-posed inverse problems, Statist. Sci., 1, 502
O'Sullivan, 1986, Automatic smoothing of regression functions in generalized linear models, J. Am. Statist. Ass., 81, 96, 10.1080/01621459.1986.10478243
Parker, 1985, Discussion on ‘Some aspects of the spline smoothing approach to non-parametric regression curve fitting’ (by B. W. Silverman), J. R. Statist. Soc. B, 47, 40
Ramsay, 2003, Exploring bias in a generalized additive model for spatial air pollution data, Environ. Hlth Perspect., 111, 1283, 10.1289/ehp.6047
R Development Core Team, 2006, R 2.4.0: a Language and Environment for Statistical Computing
Skaug, 2006, Automatic approximation of the marginal likelihood in non-Gaussian hierarchical models, Computnl Statist. Data Anal., 51, 699, 10.1016/j.csda.2006.03.005
Stone, 1977, An asymptotic equivalence of choice of model by cross-validation and Akaike's criterion, J. R. Statist. Soc. B, 39, 44
Wahba, 1980, Spline bases, regularization, and generalized cross validation for solving approximation problems with large quantities of noisy data. In, Approximation Theory III
Watkins, 1991, Fundamentals of Matrix Computations
Wood, 2000, Modelling and smoothing parameter estimation with multiple quadratic penalties, J. R. Statist. Soc. B, 62, 413, 10.1111/1467-9868.00240
Wood, 2004, Stable and efficient multiple smoothing parameter estimation for generalized additive models, J. Am. Statist. Ass., 99, 673, 10.1198/016214504000000980
Xiang, 1996, A generalized approximate cross validation for smoothing splines with non-Gaussian data, Statist. Sin., 6, 675