Download or read book Smoothing Spline ANOVA Models written by Chong Gu and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Smoothing Spline ANOVA Models written by Chong Gu and published by Springer Science & Business Media. This book was released on 2013-01-26 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Robust Designs for Smoothing Spline Anova Models written by Rong-xian Yue and published by . This book was released on 1997 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Smoothing Spline ANOVA Models and Their Applications in Complex and Massive Datasets written by Jingyi Zhang and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex and massive datasets can be easily accessed using the newly developed data acquisition technology. In spite of the fact that the smoothing spline ANOVA models have proven to be useful in a variety of fields, these datasets impose the challenges on the applications of the models. In this chapter, we present a selected review of the smoothing spline ANOVA models and highlight some challenges and opportunities in massive datasets. We review two approaches to significantly reduce the computational costs of fitting the model. One real case study is used to illustrate the performance of the reviewed methods.
Download or read book Smoothing Splines written by Yuedong Wang and published by CRC Press. This book was released on 2011-06-22 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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, t
Download or read book Computationally Efficient Kalman Filter Approaches for Fitting Smoothing Splines written by Xiaoxiao Sun and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Smoothing spline models have shown to be effective in various fields (e.g., engineering and biomedical sciences) for understanding complex signals from noisy data. As nonparametric models, smoothing spline ANOVA (Analysis Of variance) models do not fix the structure of the regression function, leading to more flexible model estimates (e.g., linear or nonlinear estimates). The functional ANOVA decomposition of the regression function estimates offers interpretable results that describe the relationship between the outcome variable, and the main and interaction effects of different covariates/predictors. However, smoothing spline ANOVA (SS-ANOVA) models suffer from high computational costs, with a computational complexity of ON3 for N observations. Various numerical approaches can address this problem. In this chapter, we focus on the introduction to a state space representation of SS-ANOVA models. The estimation algorithms based on the Kalman filter are implemented within the SS-ANOVA framework using the state space representation, reducing the computational costs significantly.
Download or read book Bayesian Smoothing Spline Analysis of Variance Models written by Chin-I. Cheng and published by . This book was released on 2009 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the pioneering work by Wahba (1990) in smoothing splines for nonparametric regression, Gu (2002) decomposed the regression function based on a tensor sum decomposition of inner product spaces into orthogonal subspaces so the estimated functions from each subspaces can be viewed separately. This is based on an ANOVA type decomposition and is called the smoothing spline ANOVA (SSANOVA) model. Current research related to smoothing spline ANOVA focuses on the frequentist approach for statistical inference in estimation and prediction. In this dissertation, we apply a fully Bayesian approach in SSANOVA to extend statistical inference not only for estimation and prediction but to model testing and selection. The prior selected for the smoothing parameter in level effects is a variant of the Zellner-Siow prior. Two sets of priors, the Pareto and the scaled [chi]21, are used for the smoothing parameters corresponding to smooth effects. We study this fully Bayesian SSANOVA model for Gaussian response variables and also extend it to generalized additive models with binary response variables.
Download or read book Nonparametric Regression and Spline Smoothing Second Edition written by Randall L. Eubank and published by CRC Press. This book was released on 1999-02-09 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a unified account of the most popular approaches to nonparametric regression smoothing. This edition contains discussions of boundary corrections for trigonometric series estimators; detailed asymptotics for polynomial regression; testing goodness-of-fit; estimation in partially linear models; practical aspects, problems and methods for confidence intervals and bands; local polynomial regression; and form and asymptotic properties of linear smoothing splines.
Download or read book Backfitting in Smoothing Spline Anova with Application to Historical Global Temperature Data written by Zhenren Luo and published by . This book was released on 1996 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Generalized Additive Models written by Simon Wood and published by CRC Press. This book was released on 2006-02-27 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Topics in Splines and Applications written by Young Kinh-Nhue Truong and published by BoD – Books on Demand. This book was released on 2018-06-06 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Splines provide a significant tool for the design of computationally economical curves and surfaces for the construction of various objects like automobiles, ship hulls, airplane fuselages and wings, propeller blades, shoe insoles, bottles, etc. It also contributes in the description of geological, physical, statistical, and even medical phenomena. Spline methods have proven to be indispensable in a variety of modern industries, including computer vision, robotics, signal and image processing, visualization, textile, graphic designs, and even media. This book aims to provide a valuable source on splines and their applications. It focuses on collecting and disseminating information in various disciplines including computer-aided geometric design, computer graphics, data visualization, data fitting, power systems, clinical and epidemiologic studies, disease detection, regression curves, social media, and biological studies. The book is useful for researchers, scientists, practitioners, and many others who seek state-of-the-art techniques and applications using splines. It is also useful for undergraduate senior students as well as graduate students in the areas of computer science, engineering, health science, statistics, and mathematics. Each chapter also provides useful information on software developments and their extensions.
Download or read book Markov Chain Monte Carlo Stochastic Approximation Algorithms Smoothing Spline ANOVA Frailty Models and Applications written by Yihua Jiang and published by . This book was released on 2009 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis contains three parts: (I) potential problems in the implementation of the Markov Chain Monte Carlo Stochastic Approximation Algorithms (MCMCSAA), remedies and new adaptive algorithms; (II) Smoothing Spline ANOVA (SS ANOVA) frailty models; and (III) application of methods in the first two parts to investigate hormone generating mechanisms.
Download or read book Multivariate Time Series Analysis and Applications written by William W. S. Wei and published by John Wiley & Sons. This book was released on 2019-03-18 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: An essential guide on high dimensional multivariate time series including all the latest topics from one of the leading experts in the field Following the highly successful and much lauded book, Time Series Analysis—Univariate and Multivariate Methods, this new work by William W.S. Wei focuses on high dimensional multivariate time series, and is illustrated with numerous high dimensional empirical time series. Beginning with the fundamentalconcepts and issues of multivariate time series analysis,this book covers many topics that are not found in general multivariate time series books. Some of these are repeated measurements, space-time series modelling, and dimension reduction. The book also looks at vector time series models, multivariate time series regression models, and principle component analysis of multivariate time series. Additionally, it provides readers with information on factor analysis of multivariate time series, multivariate GARCH models, and multivariate spectral analysis of time series. With the development of computers and the internet, we have increased potential for data exploration. In the next few years, dimension will become a more serious problem. Multivariate Time Series Analysis and its Applications provides some initial solutions, which may encourage the development of related software needed for the high dimensional multivariate time series analysis. Written by bestselling author and leading expert in the field Covers topics not yet explored in current multivariate books Features classroom tested material Written specifically for time series courses Multivariate Time Series Analysis and its Applications is designed for an advanced time series analysis course. It is a must-have for anyone studying time series analysis and is also relevant for students in economics, biostatistics, and engineering.
Download or read book Spline Regression Models written by Lawrence C. Marsh and published by SAGE. This book was released on 2001-09-14 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spline Regression Models shows how to use dummy variables to formulate and estimate spline regression models both in situations where the number and location of the spline knots are known in advance, and where estimation is required.
Download or read book System Identification Environmental Modelling and Control System Design written by Liuping Wang and published by Springer Science & Business Media. This book was released on 2011-10-20 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to Prof. Peter Young on his 70th birthday. Professor Young has been a pioneer in systems and control, and over the past 45 years he has influenced many developments in this field. This volume comprises a collection of contributions by leading experts in system identification, time-series analysis, environmetric modelling and control system design – modern research in topics that reflect important areas of interest in Professor Young’s research career. Recent theoretical developments in and relevant applications of these areas are explored treating the various subjects broadly and in depth. The authoritative and up-to-date research presented here will be of interest to academic researcher in control and disciplines related to environmental research, particularly those to with water systems. The tutorial style in which many of the contributions are composed also makes the book suitable as a source of study material for graduate students in those areas.
Download or read book Modelling Aspects of Water Framework Directive Implementation written by Peter A. Vanrolleghem and published by IWA Publishing. This book was released on 2010-04-30 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special Offer: Water Framework Directive Series Set. To buy all four titles including Volume 3 and save £100, visit: http://iwapublishing.com/books/9781780400013/water-framework-directive-series-set Modelling Aspects of Water Framework Directive Implementation: Volume 1 is a concrete outcome from the Harmoni-CA concerted action as part of a 4-volume series of Guidance Reports that guide water professionals through the implementation process of the Water Framework Directive, with a focus on the use of ICT-tools (and in particular modelling). They are complementary to the Guidance Documents produced by the EU Directorate General for Environment. Water resources planning and management and the development of appropriate policies require methodologies and tools that are able to support systematic, integrative and multidisciplinary assessments at various scales. It also requires the quantification of various uncertainties in both data and models, and the incorporation of stakeholders participation and institutional mechanisms into the various tools and risk assessment methodologies, to help decision makers understand and evaluate alternative measures and decisions. The other three volumes in the Water Framework Directive Series are: Water Framework Directive: Model supported Implementation - A Water Manager’s Guide edited by Fred Hattermann and Zbigniew W Kundzewicz Integrated Assessment for WFD implementation: Data, economic and human dimension - Volume 2, edited by Peter A. Vanrolleghem Decision support for WFD implementation - Volume 3, edited by Peter A. Vanrolleghem. Visit the IWA WaterWiki to read and share material related to this title: http://www.iwawaterwiki.org/xwiki/bin/view/Articles/IntegratedAssessmentforWaterFrameworkDirectiveImplementation
Download or read book Partially Linear Models written by Wolfgang Härdle and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last ten years, there has been increasing interest and activity in the general area of partially linear regression smoothing in statistics. Many methods and techniques have been proposed and studied. This monograph hopes to bring an up-to-date presentation of the state of the art of partially linear regression techniques. The emphasis is on methodologies rather than on the theory, with a particular focus on applications of partially linear regression techniques to various statistical problems. These problems include least squares regression, asymptotically efficient estimation, bootstrap resampling, censored data analysis, linear measurement error models, nonlinear measurement models, nonlinear and nonparametric time series models.
