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 317 articles , 3 standard articles )

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  1. Bartel, Felix; Hielscher, Ralf: Concentration inequalities for cross-validation in scattered data approximation (2022)
  2. Bartel, Felix; Potts, Daniel; Schmischke, Michael: Grouped transformations and regularization in high-dimensional explainable ANOVA approximation (2022)
  3. Fan, Ruzong; Fang, Hong-Bin: Stochastic functional linear models and Malliavin calculus (2022)
  4. Hertrich, Johannes; Ba, Fatima Antarou; Steidl, Gabriele: Sparse mixture models inspired by ANOVA decompositions (2022)
  5. Huang, Yunxiang; Wang, Qihua: A functional information criterion for region selection in functional linear models (2022)
  6. Mukhopadhyay, Minerva; Bhattacharya, Sourabh: Bayes factor asymptotics for variable selection in the Gaussian process framework (2022)
  7. Nanshan, Muye; Zhang, Nan; Xun, Xiaolei; Cao, Jiguo: Dynamical modeling for non-Gaussian data with high-dimensional sparse ordinary differential equations (2022)
  8. Zamani, Abbas-Ali; Etedali, Sadegh: Seismic response prediction of open- and closed-loop structural control systems using a multi-state-dependent parameter estimation approach (2022)
  9. Barrientos, Andrés F.; Canale, Antonio: A Bayesian goodness-of-fit test for regression (2021)
  10. Bower, Hannah; Crowther, Michael J.; Rutherford, Mark J.; Andersson, Therese M.-L.; Clements, Mark; Liu, Xing-Rong; Dickman, Paul W.; Lambert, Paul C.: Capturing simple and complex time-dependent effects using flexible parametric survival models: a simulation study (2021)
  11. Cui, Erjia; Crainiceanu, Ciprian M.; Leroux, Andrew: Additive functional Cox model (2021)
  12. Feischl, Michael; Scaglioni, Andrea: Convergence of adaptive stochastic collocation with finite elements (2021)
  13. Helwig, Nathaniel E.: Spectrally sparse nonparametric regression via elastic net regularized smoothers (2021)
  14. Huang, Hanwen; Yang, Qinglong: Large dimensional analysis of general margin based classification methods (2021)
  15. Huang, Jianhua Z.; Su, Ya: Asymptotic properties of penalized spline estimators in concave extended linear models: rates of convergence (2021)
  16. Huang, Longlong; Kopciuk, Karen; Lu, Xuewen: A group bridge approach for component selection in nonparametric accelerated failure time additive regression model (2021)
  17. Jadhav, Sneha; Ma, Chenjin; Jiang, Yefei; Shia, Ben-Chang; Ma, Shuangge: Pan-disease clustering analysis of the trend of period prevalence (2021)
  18. Kalogridis, Ioannis; Van Aelst, Stefan: (M)-type penalized splines with auxiliary scale estimation (2021)
  19. Klein, Nadja; Carlan, Manuel; Kneib, Thomas; Lang, Stefan; Wagner, Helga: Bayesian effect selection in structured additive distributional regression models (2021)
  20. Kounchev, O.; Render, H.: Error estimates for interpolation with piecewise exponential splines of order two and four (2021)

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