Smoothing spline ANOVA models Nonparametric function estimation with stochastic data, otherwise known as smoothing, has been studied by several generations of statisticians. Assisted by the recent availability of ample desktop and laptop computing power, smoothing methods are now finding their ways into everyday data analysis by practitioners. While scores of methods have proved successful for univariate smoothing, ones practical in multivariate settings number far less. Smoothing spline ANOVA models are a versatile family of smoothing methods derived through roughness penalties that are suitable for both univariate and multivariate problems. In this book, the author presents a comprehensive treatment of penalty smoothing under a unified framework. Methods are developed for (i) regression with Gaussian and non-Gaussian responses as well as with censored life time data; (ii) density and conditional density estimation under a variety of sampling schemes; and (iii) hazard rate estimation with censored life time data and covariates. The unifying themes are the general penalized likelihood method and the construction of multivariate models with built-in ANOVA decompositions. Extensive discussions are devoted to model construction, smoothing parameter selection, computation, and asymptotic convergence. Most of the computational and data analytical tools discussed in the book are implemented in R, an open-source clone of the popular S/S- PLUS language. Code for regression has been distributed in the R package gss freely available through the Internet on CRAN, the Comprehensive R Archive Network. The use of gss facilities is illustrated in the book through simulated and real data examples. (Source:

References in zbMATH (referenced in 293 articles , 3 standard articles )

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  1. Welham, Sue J.; Cullis, Brian R.; Kenward, Michael G.; Thompson, Robin: The analysis of longitudinal data using mixed model (L)-splines (2006)
  2. Wood, Simon N.: Low-rank scale-invariant tensor product smooths for generalized additive mixed models (2006)
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  4. Wood, Simon N.: Generalized additive models. An introduction with R. (2006)
  5. Clements, Mark S.; Armstrong, Bruce K.; Moolgavkar, Suresh H.: Lung cancer rate predictions using generalized additive models (2005)
  6. Fu, Wenjiang J.: Nonlinear GCV and quasi-GCV for shrinkage models (2005)
  7. Gu, Chong; Ma, Ping: Optimal smoothing in nonparametric mixed-effect models (2005)
  8. Honda, Toshio: Estimation in additive Cox models by marginal integration (2005)
  9. Ma, Shuangge; Kosorok, Michael R.: Robust semiparametric M-estimation and the weighted bootstrap (2005)
  10. Savić, Danka; Jelić, Smiljana: A mathematical model of the hypothalamo-pituitary-adrenocortical system and its stability analysis (2005)
  11. Tong, Tiejun; Wang, Yuedong: Estimating residual variance in nonparametric regression using least squares (2005)
  12. Abramovich, Felix; Antoniadis, Anestis; Sapatinas, Theofanis; Vidakovic, Brani: Optimal testing in a fixed-effects functional analysis of variance model (2004)
  13. Altman, Naomi S.; Villarreal, Julio C.: Self-modelling regression for longitudinal data with time-invariant covariates (2004)
  14. Berhane, Kiros; Gauderman, W. James; Stram, Daniel O.; Thomas, Duncan C.: Statistical issues in studies of the long-term effects of air pollution: the Southern California Children’s Health Study (with comments and rejoinder) (2004)
  15. Berlinet, Alain; Thomas-Agnan, Christine: Reproducing kernel Hilbert spaces in probability and statistics. With a preface by Persi Diaconis. (2004)
  16. Chang, Xiao-Wen; Qu, Leming: Wavelet estimation of partially linear models (2004)
  17. Ferris, Michael C.; Voelker, Meta M.; Zhang, Hao Helen: Model building with likelihood basis pursuit (2004)
  18. Gu, Chong: Model diagnostics for smoothing spline ANOVA models (2004)
  19. Kim, Young-Ju; Gu, Chong: Smoothing spline Gaussian regression: more scalable computation via efficient approximation (2004)
  20. Lin, Yi; Brown, Lawrence D.: Statistical properties of the method of regularization with periodic Gaussian reproducing kernel (2004)

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