Smoothing Spline ANOVA Models

Abstract

Nonparametric function estimation with stochastic data, otherwiseknown as smoothing, has been studied by several generations ofstatisticians. Assisted by the ample computing power in today'sservers, desktops, and laptops, smoothing methods have been findingtheir ways into everyday data analysis by practitioners. While scoresof methods have proved successful for univariate smoothing, onespractical in multivariate settings number far less. Smoothing splineANOVA models are a versatile family of smoothing methods derivedthrough roughness penalties, that are suitable for both univariate andmultivariate problems.In this book, the author presents a treatise on penalty smoothingunder a unified framework. Methods are developed for (i) regressionwith Gaussian and non-Gaussian responses as well as with censored lifetime data; (ii) density and conditional density estimation under avariety of sampling schemes; and (iii) hazard rate estimation withcensored life time data and covariates. The unifying themes are thegeneral penalized likelihood method and the construction ofmultivariate models with built-in ANOVA decompositions. Extensivediscussions are devoted to model construction, smoothing parameterselection, computation, and asymptotic convergence.