Smoothing Splines

Author: Yuedong Wang
Publisher: CRC Press
ISBN: 1420077562
Format: PDF, Kindle
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A general class of powerful and flexible modeling techniques, spline smoothing has attracted a great deal of research attention in recent years and has been widely used in many application areas, from medicine to economics. Smoothing Splines: Methods and Applications covers basic smoothing spline models, including polynomial, periodic, spherical, thin-plate, L-, and partial splines, as well as more advanced models, such as smoothing spline ANOVA, extended and generalized smoothing spline ANOVA, vector spline, nonparametric nonlinear regression, semiparametric regression, and semiparametric mixed-effects models. It also presents methods for model selection and inference. The book provides unified frameworks for estimation, inference, and software implementation by using the general forms of nonparametric/semiparametric, linear/nonlinear, and fixed/mixed smoothing spline models. The theory of reproducing kernel Hilbert space (RKHS) is used to present various smoothing spline models in a unified fashion. Although this approach can be technical and difficult, the author makes the advanced smoothing spline methodology based on RKHS accessible to practitioners and students. He offers a gentle introduction to RKHS, keeps theory at a minimum level, and explains how RKHS can be used to construct spline models. Smoothing Splines offers a balanced mix of methodology, computation, implementation, software, and applications. It uses R to perform all data analyses and includes a host of real data examples from astronomy, economics, medicine, and meteorology. The codes for all examples, along with related developments, can be found on the book’s web page.

Nonparametric Regression and Generalized Linear Models

Author: P.J. Green
Publisher: CRC Press
ISBN: 9780412300400
Format: PDF, Kindle
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In recent years, there has been a great deal of interest and activity in the general area of nonparametric smoothing in statistics. This monograph concentrates on the roughness penalty method and shows how this technique provides a unifying approach to a wide range of smoothing problems. The method allows parametric assumptions to be realized in regression problems, in those approached by generalized linear modelling, and in many other contexts. The emphasis throughout is methodological rather than theoretical, and it concentrates on statistical and computation issues. Real data examples are used to illustrate the various methods and to compare them with standard parametric approaches. Some publicly available software is also discussed. The mathematical treatment is self-contained and depends mainly on simple linear algebra and calculus. This monograph will be useful both as a reference work for research and applied statisticians and as a text for graduate students and other encountering the material for the first time.

Local Polynomial Modelling and Its Applications

Author: Jianqing Fan
Publisher: CRC Press
ISBN: 9780412983214
Format: PDF, ePub, Docs
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Data-analytic approaches to regression problems, arising from many scientific disciplines are described in this book. The aim of these nonparametric methods is to relax assumptions on the form of a regression function and to let data search for a suitable function that describes the data well. The use of these nonparametric functions with parametric techniques can yield very powerful data analysis tools. Local polynomial modeling and its applications provides an up-to-date picture on state-of-the-art nonparametric regression techniques. The emphasis of the book is on methodologies rather than on theory, with a particular focus on applications of nonparametric techniques to various statistical problems. High-dimensional data-analytic tools are presented, and the book includes a variety of examples. This will be a valuable reference for research and applied statisticians, and will serve as a textbook for graduate students and others interested in nonparametric regression.

Sustainable Electrical Power Resources through Energy Optimization and Future Engineering

Author: Shaharin Anwar Sulaiman
Publisher: Springer
ISBN: 9811304351
Format: PDF, Docs
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This book presents recent science and engineering research in the field of conventional and renewable energy, energy efficiency and optimization, discussing problems such as availability, peak load and reliability of sustainable supply for power to consumers. Such research is imperative since efficient and environmentally friendly solutions are critical in modern electricity production and transmission.

Mathematische Modellbildung und Simulation

Author: Marco Günther
Publisher: John Wiley & Sons
ISBN: 3527686509
Format: PDF, ePub, Mobi
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Diese f?r Studierende ebenso wie f?r Wissenschaftler, Ingenieure und Praktiker geeignete Einf?hrung in mathematische Modellbildung und Simulation setzt nur einfache Grundkenntnisse in Analysis und linearer Algebra voraus - alle weiteren Konzepte werden im Buch entwickelt. Die Leserinnen und Leser lernen anhand detailliert besprochener Beispiele aus unterschiedlichsten Bereichen (Biologie, ?kologie, ?konomie, Medizin, Landwirtschaft, Chemie, Maschinenbau, Elektrotechnik, Prozesstechnik usw.), sich kritisch mit mathematischen Modellen auseinanderzusetzen und anspruchsvolle mathematische Modelle selbst zu formulieren und zu implementieren. Das Themenspektrum reicht von statistischen Modellen bis zur Mehrphasen-Str?mungsdynamik in 3D. F?r alle im Buch besprochenen Modellklassen wird kostenlose Open-Source-Software zur Verf?gung gestellt. Grundlage ist das eigens f?r dieses Buch entwickelte Betriebssystem Gm.Linux ("Geisenheim-Linux"), das ohne Installationsaufwand z.B. auch auf Windows-Rechnern l?uft. Ein Referenzkartensystem zu Gm.Linux mit einfachen Schritt-f?r-Schritt-Anleitungen erm?glicht es, auch komplexe statistische Berechnungen oder 3D-Str?mungssimulationen in kurzer Zeit zu realisieren. Alle im Buch beschriebenen Verfahren beziehen sich auf Gm.Linux 2.0 (und die darin fixierten Versionen aller Anwendungsprogramme) und sind daher unabh?ngig von Softwareaktualisierungen langfristig verwendbar.

Generalized Additive Models

Author: Simon Wood
Publisher: CRC Press
ISBN: 1584884746
Format: PDF
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Now in widespread use, generalized additive models (GAMs) have evolved into a standard statistical methodology of considerable flexibility. While Hastie and Tibshirani's outstanding 1990 research monograph on GAMs is largely responsible for this, there has been a long-standing need for an accessible introductory treatment of the subject that also emphasizes recent penalized regression spline approaches to GAMs and the mixed model extensions of these models. Generalized Additive Models: An Introduction with R imparts a thorough understanding of the theory and practical applications of GAMs and related advanced models, enabling informed use of these very flexible tools. The author bases his approach on a framework of penalized regression splines, and builds a well-grounded foundation through motivating chapters on linear and generalized linear models. While firmly focused on the practical aspects of GAMs, discussions include fairly full explanations of the theory underlying the methods. Use of the freely available R software helps explain the theory and illustrates the practicalities of linear, generalized linear, and generalized additive models, as well as their mixed effect extensions. The treatment is rich with practical examples, and it includes an entire chapter on the analysis of real data sets using R and the author's add-on package mgcv. Each chapter includes exercises, for which complete solutions are provided in an appendix. Concise, comprehensive, and essentially self-contained, Generalized Additive Models: An Introduction with R prepares readers with the practical skills and the theoretical background needed to use and understand GAMs and to move on to other GAM-related methods and models, such as SS-ANOVA, P-splines, backfitting and Bayesian approaches to smoothing and additive modelling.

Spline Models for Observational Data

Author: Grace Wahba
Publisher: SIAM
ISBN: 0898712440
Format: PDF, ePub
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This book serves well as an introduction into the more theoretical aspects of the use of spline models. It develops a theory and practice for the estimation of functions from noisy data on functionals. The simplest example is the estimation of a smooth curve, given noisy observations on a finite number of its values. Convergence properties, data based smoothing parameter selection, confidence intervals, and numerical methods are established which are appropriate to a number of problems within this framework. Methods for including side conditions and other prior information in solving ill posed inverse problems are provided. Data which involves samples of random variables with Gaussian, Poisson, binomial, and other distributions are treated in a unified optimization context. Experimental design questions, i.e., which functionals should be observed, are studied in a general context. Extensions to distributed parameter system identification problems are made by considering implicitly defined functionals.

Gaussian Markov Random Fields

Author: Havard Rue
Publisher: CRC Press
ISBN: 9780203492024
Format: PDF, Mobi
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Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studies and, online, a c-library for fast and exact simulation. With chapters contributed by leading researchers in the field, this volume is essential reading for statisticians working in spatial theory and its applications, as well as quantitative researchers in a wide range of science fields where spatial data analysis is important.

Statistical Computing with R

Author: Maria L. Rizzo
Publisher: CRC Press
ISBN: 1584885459
Format: PDF, ePub
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Computational statistics and statistical computing are two areas that employ computational, graphical, and numerical approaches to solve statistical problems, making the versatile R language an ideal computing environment for these fields. One of the first books on these topics to feature R, Statistical Computing with R covers the traditional core material of computational statistics, with an emphasis on using the R language via an examples-based approach. Suitable for an introductory course in computational statistics or for self-study, it includes R code for all examples and R notes to help explain the R programming concepts. After an overview of computational statistics and an introduction to the R computing environment, the book reviews some basic concepts in probability and classical statistical inference. Each subsequent chapter explores a specific topic in computational statistics. These chapters cover the simulation of random variables from probability distributions, the visualization of multivariate data, Monte Carlo integration and variance reduction methods, Monte Carlo methods in inference, bootstrap and jackknife, permutation tests, Markov chain Monte Carlo (MCMC) methods, and density estimation. The final chapter presents a selection of examples that illustrate the application of numerical methods using R functions. Focusing on implementation rather than theory, this text serves as a balanced, accessible introduction to computational statistics and statistical computing.

Analysis of Variance for Functional Data

Author: Jin-Ting Zhang
Publisher: CRC Press
ISBN: 1439862745
Format: PDF, Kindle
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Despite research interest in functional data analysis in the last three decades, few books are available on the subject. Filling this gap, Analysis of Variance for Functional Data presents up-to-date hypothesis testing methods for functional data analysis. The book covers the reconstruction of functional observations, functional ANOVA, functional linear models with functional responses, ill-conditioned functional linear models, diagnostics of functional observations, heteroscedastic ANOVA for functional data, and testing equality of covariance functions. Although the methodologies presented are designed for curve data, they can be extended to surface data. Useful for statistical researchers and practitioners analyzing functional data, this self-contained book gives both a theoretical and applied treatment of functional data analysis supported by easy-to-use MATLAB® code. The author provides a number of simple methods for functional hypothesis testing. He discusses pointwise, L2-norm-based, F-type, and bootstrap tests. Assuming only basic knowledge of statistics, calculus, and matrix algebra, the book explains the key ideas at a relatively low technical level using real data examples. Each chapter also includes bibliographical notes and exercises. Real functional data sets from the text and MATLAB codes for analyzing the data examples are available for download from the author’s website.