Smoothing Spline ANOVA Models (Springer Series in Statistics)

Smoothing methods are an active area of research. 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. 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.

Nonparametric function estimation with stochastic data, otherwise

known as smoothing, has been studied by several generations of

statisticians. Assisted by the ample computing power in today's

servers, desktops, and laptops, smoothing methods have been 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 treatise on penalty smoothing

under a unified framework. Methods are developed for (i) regression

with Gaussian and non-Gaussian responses as well as with censored lifetime 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.