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. Wood, Simon N.: Stable and efficient multiple smoothing parameter estimation for generalized additive models (2004)
  2. Yuan, Ming; Wahba, Grace: Doubly penalized likelihood estimator in heteroscedastic regression (2004)
  3. Zhang, Hao Helen; Wahba, Grace; Lin, Yi; Voelker, Meta; Ferris, Michael; Klein, Ronald; Klein, Barbara: Variable selection and model building via likelihood basis pursuit (2004)
  4. Wang, Yuedong; Ke, Chunlei; Brown, Morton B.: Shape-invariant modeling of circadian rhythms with random effects and smoothing spline ANOVA decompositions (2003)
  5. Wood, Simon N.: Thin plate regression splines (2003)
  6. Gu, Chong: Smoothing spline ANOVA models (2002)
  7. Gu, Chong; Kim, Young-Ju: Penalized likelihood regression: General formulation and efficient approximation (2002)
  8. Wahba, Grace: Soft and hard classification by reproducing kernel Hilbert space methods (2002)
  9. Yue, Rong-Xian; Hickernell, F. J.: Designs for smoothing spline ANOVA models (2002)
  10. Opsomer, Jean; Wang, Yuedong; Yang, Yuhong: Nonparametric regression with correlated errors. (2001)
  11. Lin, Xiwu; Wahba, Grace; Xiang, Dong; Gao, Fangyu; Klein, Ronald: Smoothing spline ANOVA models for large data sets with Bernoulli observations and the randomized GACV. (2000)
  12. Luo, Zhen: Backfitting in smoothing spline ANOVA (1998)
  13. Wang, Yuedong: GRKPACK: Fitting smoothing spline ANOVA models for exponential families (1997)

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