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Here is a clear exposition of nonparametric smoothing methods for statisticians. The focus is applied rather than theoretical, with a large number of illustrations from different disciplines.

Mathematical statistics --- Smoothing (Statistics) --- Smoothing (Statistics). --- Basic Sciences. Statistics --- Experimental Design. --- 519.5 --- Curve fitting --- Graduation (Statistics) --- Roundoff errors --- Statistics

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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.

Mathematical statistics --- Analysis of variance --- Spline theory --- Smoothing (Statistics) --- #PBIB:2003.4 --- Spline functions --- ANOVA (Analysis of variance) --- Variance analysis --- Approximation theory --- Interpolation --- Curve fitting --- Graduation (Statistics) --- Roundoff errors --- Statistics --- Experimental design --- Probabilities. --- Statistics . --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Risk

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The The primary primary aim aim of of this this book book is is to to explore explore the the use use of of nonparametric nonparametric regres­ regres­ sion sion (i. e. , (i. e. , smoothing) smoothing) methodology methodology in in testing testing the the fit fit of of parametric parametric regression regression models. models. It It is is anticipated anticipated that that the the book book will will be be of of interest interest to to an an audience audience of of graduate graduate students, students, researchers researchers and and practitioners practitioners who who study study or or use use smooth­ smooth­ ing ing methodology. methodology. Chapters Chapters 2-4 2-4 serve serve as as a a general general introduction introduction to to smoothing smoothing in in the the case case of of a a single single design design variable. variable. The The emphasis emphasis in in these these chapters chapters is is on on estimation estimation of of regression regression curves, curves, with with hardly hardly any any mention mention of of the the lack-of­ lack-of­ fit fit problem. problem. As As such, such, Chapters Chapters 2-4 2-4 could could be be used used as as the the foundation foundation of of a a graduate graduate level level statistics statistics course course on on nonparametric nonparametric regression. regression.

Mathematical statistics --- Smoothing (Statistics) --- Nonparametric statistics. --- Goodness-of-fit tests. --- Lissage (Statistique) --- Statistique non-paramétrique --- Goodness-of-fit tests --- Nonparametric statistics --- 519.2 --- Curve fitting --- Graduation (Statistics) --- Roundoff errors --- Statistics --- Distribution-free statistics --- Statistics, Distribution-free --- Statistics, Nonparametric --- Tests, Goodness-of-fit --- Statistical hypothesis testing --- Probability. Mathematical statistics --- 519.2 Probability. Mathematical statistics --- Statistique non-paramétrique --- Applied mathematics. --- Engineering mathematics. --- Applications of Mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematics

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Mathematical statistics --- Smoothing (Statistics) --- Statistique mathématique --- Lissage (Statistique) --- Data processing --- Informatique --- 519.246 --- -Smoothing (Statistics) --- AA / International- internationaal --- 303.0 --- Curve fitting --- Graduation (Statistics) --- Roundoff errors --- Statistics --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Probabilities --- Sampling (Statistics) --- Statistics of stochastic processes. Estimation of stochastic processes. Hypothesis testing. Statistics of point processes. Time series analysis. Auto-correlation. Regression --- Statistische technieken in econometrie. Wiskundige statistiek (algemene werken en handboeken). --- Statistical methods --- Data processing. --- Smoothing (Statistics). --- 519.246 Statistics of stochastic processes. Estimation of stochastic processes. Hypothesis testing. Statistics of point processes. Time series analysis. Auto-correlation. Regression --- Statistique mathématique --- Statistische technieken in econometrie. Wiskundige statistiek (algemene werken en handboeken) --- Statistique non paramétrique --- Mathematical statistics - Data processing