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. Belitz, Christiane: Model selection in generalised structured additive regression models. (2007)
  2. Cao, Jiguo; Ramsay, James O.: Parameter cascades and profiling in functional data analysis (2007)
  3. D. Stasinopoulos; Robert Rigby: Generalized Additive Models for Location Scale and Shape (GAMLSS) in R (2007) not zbMATH
  4. Fan, Jianqing; Jiang, Jiancheng: Nonparametric inference with generalized likelihood ratio tests (With comments and rejoinder) (2007)
  5. Gill, Ryan; Lee, Kiseop; Song, Seongjoo: Computation of estimates in segmented regression and a liquidity effect model (2007)
  6. Leng, Chenlei; Ma, Shuangge: Accelerated failure time models with nonlinear covariates effects (2007)
  7. Liu, Anna; Wang, Yuedong: Modeling of hormone secretion-generating mechanisms with splines: a pseudo-likelihood approach (2007)
  8. Liu, Dawei; Lin, xihong; Ghosh, Debashis: Semiparametric regression of multidimensional genetic pathway data: Least-squares kernel machines and linear mixed models (2007)
  9. Li, Youjuan; Liu, Yufeng; Zhu, Ji: Quantile regression in reproducing kernel Hilbert spaces (2007)
  10. Abramovich, Felix; Angelini, Claudia: Testing in mixed-effects FANOVA models (2006)
  11. Du, Pang; Gu, Chong: Penalized likelihood hazard estimation: Efficient approximation and Bayesian confidence intervals (2006)
  12. Faraway, Julian J.: Extending the linear model with R. Generalized linear, mixed effects and nonparametric regression models. (2006)
  13. Hannig, Jan; Lee, Thomas C. M.: On Poisson signal estimation under Kullback-Leibler discrepancy and squared risk (2006)
  14. Hastie, Trevor; Zhu, Ji: Comment on: “Support vector machines with applications” (2006)
  15. Lee, Yoonkyung; Kim, Yuwon; Lee, Sangjun; Koo, Ja-Yong: Structured multicategory support vector machines with analysis of variance decomposition (2006)
  16. Leng, Chenlei; Zhang, Hao Helen: Model selection in nonparametric hazard regression (2006)
  17. Lin, Jiang; Zhang, Daowen; Davidian, Marie: Smoothing spline-based score tests for proportional hazards models (2006)
  18. Lin, Yi; Zhang, Hao Helen: Component selection and smoothing in multivariate nonparametric regression (2006)
  19. Ma, Shuangge; Kosorok, Michael R.: Adaptive penalized M-estimation with current status data (2006)
  20. Tutz, Gerhard; Binder, Harald: Generalized additive modeling with implicit variable selection by likelihood-based boosting (2006)

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