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. Li, Runze; Li, Yan: Local linear regression for data with AR errors (2009)
  2. Lu, Yiqiang; Zhang, Riquan: Smoothing spline estimation of generalised varying-coefficient mixed model (2009)
  3. Ni, Xiao; Zhang, Hao Helen; Zhang, Daowen: Automatic model selection for partially linear models (2009)
  4. Xu, Wangli; Zhu, Lixing: Kernel-based generalized cross-validation in non-parametric mixed-effect models (2009)
  5. Young, P. C.; Ratto, Marco: A unified approach to environmental systems modeling (2009)
  6. Banerjee, Sudipto; Gelfand, Alan E.; Finley, Andrew O.; Sang, Huiyan: Gaussian predictive process models for large spatial data sets (2008)
  7. Belitz, Christiane; Lang, Stefan: Simultaneous selection of variables and smoothing parameters in structured additive regression models (2008)
  8. Davison, A. C.: Some challenges for statistics (2008)
  9. Gu, Chong: Smoothing noisy data via regularization: statistical perspectives (2008)
  10. Koenker, Roger; Mizera, Ivan: Primal and dual formulations relevant for the numerical estimation of a probability density via regularization (2008)
  11. Kosorok, Michael R.: Introduction to empirical processes and semiparametric inference (2008)
  12. Lukas, Mark A.: Strong robust generalized cross-validation for choosing the regularization parameter (2008)
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  15. Nielsen, J. D.; Dean, C. B.: Clustered mixed nonhomogeneous Poisson process spline models for the analysis of recurrent event panel data (2008)
  16. Qin, Li; Wang, Yuedong: Nonparametric spectral analysis with applications to seizure characterization using EEG time series (2008)
  17. Wand, M. P.; Ormerod, J. T.: On semiparametric regression with O’Sullivan penalized splines (2008)
  18. Wang, Xiaofeng: Semiparametric mixed model for longitudinal image data (2008)
  19. Wood, Simon N.: Fast stable direct fitting and smoothness selection for generalized additive models (2008)
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