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Programming --- Numerical analysis --- 519.61 --- Matrices --- -Roundoff errors --- -681.3*G13 --- Error analysis (Mathematics) --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal --- Numerical methods of algebra --- Data processing --- Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- Fishes --- Phenology --- Roundoff errors --- Ecology --- Physiology --- Congresses. --- Reproduction --- Data processing. --- 681.3*G13 Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 519.61 Numerical methods of algebra --- 681.3*G13

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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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This is the first book to provide an accessible and comprehensive introduction to a newly developed smoothing technique using asymmetric kernel functions. Further, it discusses the statistical properties of estimators and test statistics using asymmetric kernels. The topics addressed include the bias-variance tradeoff, smoothing parameter choices, achieving rate improvements with bias reduction techniques, and estimation with weakly dependent data. Further, the large- and finite-sample properties of estimators and test statistics smoothed by asymmetric kernels are compared with those smoothed by symmetric kernels. Lastly, the book addresses the applications of asymmetric kernel estimation and testing to various forms of nonnegative economic and financial data. Until recently, the most popularly chosen nonparametric methods used symmetric kernel functions to estimate probability density functions of symmetric distributions with unbounded support. Yet many types of economic and financial data are nonnegative and violate the presumed conditions of conventional methods. Examples include incomes, wages, short-term interest rates, and insurance claims. Such observations are often concentrated near the boundary and have long tails with sparse data. Smoothing with asymmetric kernel functions has increasingly gained attention, because the approach successfully addresses the issues arising from distributions that have natural boundaries at the origin and heavy positive skewness. Offering an overview of recently developed kernel methods, complemented by intuitive explanations and mathematical proofs, this book is highly recommended to all readers seeking an in-depth and up-to-date guide to nonparametric estimation methods employing asymmetric kernel smoothing.

Statistics. --- Statistics for Business/Economics/Mathematical Finance/Insurance. --- Statistical Theory and Methods. --- Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law. --- Statistics and Computing/Statistics Programs. --- Smoothing (Statistics) --- Curve fitting --- Graduation (Statistics) --- Roundoff errors --- Statistics --- Mathematical statistics. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Statistics for Social Sciences, Humanities, Law. --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Probabilities --- Sampling (Statistics) --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Statistics .

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Business forecasting --- Smoothing (Statistics) --- Regression analysis --- Prévision commerciale --- Lissage (Statistique) --- Analyse de régression --- Statistical methods --- Méthodes statistiques --- Regression Analysis --- AA / International- internationaal --- 331.061 --- 304.5 --- 65.012.23 --- -Smoothing (Statistics) --- Analysis, Regression --- Linear regression --- Regression modeling --- Multivariate analysis --- Structural equation modeling --- Curve fitting --- Graduation (Statistics) --- Roundoff errors --- Statistics --- Business --- Business forecasts --- Forecasting, Business --- Business cycles --- Economic forecasting --- Economische vooruitzichten. --- Techniek van de statistische-econometrische voorspellingen. Prognose in de econometrie. --- Prediction of development. Business forecasting --- Forecasting --- 65.012.23 Prediction of development. Business forecasting --- Prévision commerciale --- Analyse de régression --- Méthodes statistiques --- Statistical methods. --- Techniek van de statistische-econometrische voorspellingen. Prognose in de econometrie --- Economische vooruitzichten --- Business forecasting - Statistical methods