Smoothing Spline ANOVA Models

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<p>Nonparametric function estimation with stochastic data, otherwise</p><p>known as smoothing, has been studied by several generations of</p><p>statisticians. Assisted by the ample computing power in today's</p><p>servers, desktops, and laptops, smoothing methods have been finding</p><p>their ways into everyday data analysis by practitioners. While scores</p><p>of methods have proved successful for univariate smoothing, ones</p><p>practical in multivariate settings number far less. Smoothing spline</p><p>ANOVA models are a versatile family of smoothing methods derived</p><p>through roughness penalties, that are suitable for both univariate and</p><p>multivariate problems.</p><p>In this book, the author presents a treatise on penalty smoothing</p><p>under a unified framework. Methods are developed for (i) regression</p><p>with Gaussian and non-Gaussian responses as well as with censored lifetime data; (ii) density and conditional density estimation under a</p><p>variety of sampling schemes; and (iii) hazard rate estimation with</p><p>censored life time data and covariates. The unifying themes are the</p><p>general penalized likelihood method and the construction of</p><p>multivariate models with built-in ANOVA decompositions. Extensive</p><p>discussions are devoted to model construction, smoothing parameter</p><p>selection, computation, and asymptotic convergence.</p><p>Most of the computational and data analytical tools discussed in the</p><p>book are implemented in R, an open-source platform for statistical</p><p>computing and graphics. Suites of functions are embodied in the R</p><p>package gss, and are illustrated throughout the book using simulated</p><p>and real data examples.</p><p>This monograph will be useful as a reference work for researchers in</p><p>theoretical and applied statistics as well as for those in other</p><p>related disciplines. It can also be used as a text for graduate level</p><p>courses on the subject. Most of the materials are accessible to a</p><p>second year graduate student with a good training in calculus and</p><p>linear algebra and working knowledge in basic statistical inferences</p><p>such as linear models and maximum likelihood estimates.</p>