E-Book Overview
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.
Most of the computational and data analytical tools discussed in the
book are implemented in R, an open-source platform for statistical
computing and graphics. Suites of functions are embodied in the R
package gss, and are illustrated throughout the book using simulated
and real data examples.
This monograph will be useful as a reference work for researchers in
theoretical and applied statistics as well as for those in other
related disciplines. It can also be used as a text for graduate level
courses on the subject. Most of the materials are accessible to a
second year graduate student with a good training in calculus and
linear algebra and working knowledge in basic statistical inferences
such as linear models and maximum likelihood estimates.
E-Book Content
Springer Series in Statistics Advisors: P. Bickel, P. Diggle, S. Feinberg, U. Gather, I. Olkin, S. Zeger
For further volumes: http://www.springer.com/series/692
297
Chong Gu
Smoothing Spline ANOVA Models Second Edition
123
Chong Gu Department of Statistics Purdue University West Lafayette, IN 47907 USA
ISSN 0172-7397 ISBN 978-1-4614-5368-0 ISBN 978-1-4614-5369-7 (eBook) DOI 10.1007/978-1-4614-5369-7 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2012950795 c Springer Science+Business Media New York 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable