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Author : Grace Wahba
Publisher :
ISBN 13 :
Total Pages : 169 pages
Book Rating : 4.:/5 (115 download)
Download or read book Spline Models for Observational Data written by Grace Wahba and published by . This book was released on 1990 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Grace Wahba
Publisher : SIAM
ISBN 13 : 9781611970128
Total Pages : 181 pages
Book Rating : 4.9/5 (71 download)
Download or read book Spline Models for Observational Data written by Grace Wahba and published by SIAM. This book was released on 1990-01-01 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. The estimate is a polynomial smoothing spline. By placing this smoothing problem in the setting of reproducing kernel Hilbert spaces, a theory is developed which includes univariate smoothing splines, thin plate splines in d dimensions, splines on the sphere, additive splines, and interaction splines in a single framework. A straightforward generalization allows the theory to encompass the very important area of (Tikhonov) regularization methods for ill-posed inverse problems. Convergence properties, data based smoothing parameter selection, confidence intervals, and numerical methods are established which are appropriate to a wide variety of problems which fall within this framework. Methods for including side conditions and other prior information in solving ill-posed inverse problems are included. 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.
Author : Grace Wahba
Publisher : SIAM
ISBN 13 : 0898712440
Total Pages : 174 pages
Book Rating : 4.8/5 (987 download)
Download or read book Spline Models for Observational Data written by Grace Wahba and published by SIAM. This book was released on 1990-09-01 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Charles K. Chui
Publisher : SIAM
ISBN 13 : 0898712262
Total Pages : 192 pages
Book Rating : 4.8/5 (987 download)
Download or read book Multivariate Splines written by Charles K. Chui and published by SIAM. This book was released on 1988-01-01 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Subject of multivariate splines presented from an elementary point of view; includes many open problems.
Author : Yuedong Wang
Publisher : CRC Press
ISBN 13 : 1420077562
Total Pages : 380 pages
Book Rating : 4.4/5 (2 download)
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
Author : Chong Gu
Publisher : Springer Science & Business Media
ISBN 13 : 1461453690
Total Pages : 446 pages
Book Rating : 4.4/5 (614 download)
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.
Author : Young Kinh-Nhue Truong
Publisher : BoD – Books on Demand
ISBN 13 : 1789232503
Total Pages : 162 pages
Book Rating : 4.7/5 (892 download)
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.
Author : Grace Wahba
Publisher :
ISBN 13 :
Total Pages : 4 pages
Book Rating : 4.:/5 (227 download)
Download or read book Multivariate Model Building and Model Identification written by Grace Wahba and published by . This book was released on 1990 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: A very substantial number of results were obtained during this contract in the area of multivariate model building and model identification. A list of publications in which the Air Force Contract is mentioned appears below. We are continuing this work in the follow on contract, AFOSR 90-0103. The research monograph Spline Models for Observational Data by the PI was published by The Society for Industrial and Applied Mathematics in March 1990 as volume 59 in the prestigious CBMS-NSF Regional Conference Series in Applied Mathematics. Although the actual writing of this monograph was not supported by the AFOSR, a number of research results obtained under AFOSR sponsorship are discussed in it. We have acknowledged in the Foreword the research support of the AFOSR. (kr).
Author : Dale J. Poirier
Publisher : North-Holland
ISBN 13 :
Total Pages : 224 pages
Book Rating : 4.F/5 ( download)
Download or read book The Econometrics of Structural Change, with Special Emphasis on Spline Functions written by Dale J. Poirier and published by North-Holland. This book was released on 1976 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to models of structural change; Linear splines; Cubic splines; Bilineart splines; Cobb-Douglas splines; Splines lags: why the almon lag has gone to pieces; A survey of estimation techniques for models with unknown points of structural change; The use of splines in multiple regression; Spline loss functions.
Author : Lang Wu
Publisher : CRC Press
ISBN 13 : 9781420074086
Total Pages : 431 pages
Book Rating : 4.0/5 (74 download)
Download or read book Mixed Effects Models for Complex Data written by Lang Wu and published by CRC Press. This book was released on 2009-11-11 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although standard mixed effects models are useful in a range of studies, other approaches must often be used in correlation with them when studying complex or incomplete data. Mixed Effects Models for Complex Data discusses commonly used mixed effects models and presents appropriate approaches to address dropouts, missing data, measurement errors, censoring, and outliers. For each class of mixed effects model, the author reviews the corresponding class of regression model for cross-sectional data. An overview of general models and methods, along with motivating examples After presenting real data examples and outlining general approaches to the analysis of longitudinal/clustered data and incomplete data, the book introduces linear mixed effects (LME) models, generalized linear mixed models (GLMMs), nonlinear mixed effects (NLME) models, and semiparametric and nonparametric mixed effects models. It also includes general approaches for the analysis of complex data with missing values, measurement errors, censoring, and outliers. Self-contained coverage of specific topics Subsequent chapters delve more deeply into missing data problems, covariate measurement errors, and censored responses in mixed effects models. Focusing on incomplete data, the book also covers survival and frailty models, joint models of survival and longitudinal data, robust methods for mixed effects models, marginal generalized estimating equation (GEE) models for longitudinal or clustered data, and Bayesian methods for mixed effects models. Background material In the appendix, the author provides background information, such as likelihood theory, the Gibbs sampler, rejection and importance sampling methods, numerical integration methods, optimization methods, bootstrap, and matrix algebra. Failure to properly address missing data, measurement errors, and other issues in statistical analyses can lead to severely biased or misleading results. This book explores the biases that arise when naïve methods are used and shows which approaches should be used to achieve accurate results in longitudinal data analysis.
Author : Paul H.C. Eilers
Publisher : Cambridge University Press
ISBN 13 : 1108686885
Total Pages : 213 pages
Book Rating : 4.1/5 (86 download)
Download or read book Practical Smoothing written by Paul H.C. Eilers and published by Cambridge University Press. This book was released on 2021-03-18 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a practical guide to P-splines, a simple, flexible and powerful tool for smoothing. P-splines combine regression on B-splines with simple, discrete, roughness penalties. They were introduced by the authors in 1996 and have been used in many diverse applications. The regression basis makes it straightforward to handle non-normal data, like in generalized linear models. The authors demonstrate optimal smoothing, using mixed model technology and Bayesian estimation, in addition to classical tools like cross-validation and AIC, covering theory and applications with code in R. Going far beyond simple smoothing, they also show how to use P-splines for regression on signals, varying-coefficient models, quantile and expectile smoothing, and composite links for grouped data. Penalties are the crucial elements of P-splines; with proper modifications they can handle periodic and circular data as well as shape constraints. Combining penalties with tensor products of B-splines extends these attractive properties to multiple dimensions. An appendix offers a systematic comparison to other smoothers.
Author : Genshiro Kitagawa
Publisher : Springer Science & Business Media
ISBN 13 : 1461207614
Total Pages : 265 pages
Book Rating : 4.4/5 (612 download)
Download or read book Smoothness Priors Analysis of Time Series written by Genshiro Kitagawa and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Smoothness Priors Analysis of Time Series addresses some of the problems of modeling stationary and nonstationary time series primarily from a Bayesian stochastic regression "smoothness priors" state space point of view. Prior distributions on model coefficients are parametrized by hyperparameters. Maximizing the likelihood of a small number of hyperparameters permits the robust modeling of a time series with relatively complex structure and a very large number of implicitly inferred parameters. The critical statistical ideas in smoothness priors are the likelihood of the Bayesian model and the use of likelihood as a measure of the goodness of fit of the model. The emphasis is on a general state space approach in which the recursive conditional distributions for prediction, filtering, and smoothing are realized using a variety of nonstandard methods including numerical integration, a Gaussian mixture distribution-two filter smoothing formula, and a Monte Carlo "particle-path tracing" method in which the distributions are approximated by many realizations. The methods are applicable for modeling time series with complex structures.
Author : Jaroslaw Harezlak
Publisher : Springer
ISBN 13 : 1493988530
Total Pages : 331 pages
Book Rating : 4.4/5 (939 download)
Download or read book Semiparametric Regression with R written by Jaroslaw Harezlak and published by Springer. This book was released on 2018-12-12 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This easy-to-follow applied book on semiparametric regression methods using R is intended to close the gap between the available methodology and its use in practice. Semiparametric regression has a large literature but much of it is geared towards data analysts who have advanced knowledge of statistical methods. While R now has a great deal of semiparametric regression functionality, many of these developments have not trickled down to rank-and-file statistical analysts. The authors assemble a broad range of semiparametric regression R analyses and put them in a form that is useful for applied researchers. There are chapters devoted to penalized spines, generalized additive models, grouped data, bivariate extensions of penalized spines, and spatial semi-parametric regression models. Where feasible, the R code is provided in the text, however the book is also accompanied by an external website complete with datasets and R code. Because of its flexibility, semiparametric regression has proven to be of great value with many applications in fields as diverse as astronomy, biology, medicine, economics, and finance. This book is intended for applied statistical analysts who have some familiarity with R.
Author : Xiaofeng Wang
Publisher : CRC Press
ISBN 13 : 1351165755
Total Pages : 312 pages
Book Rating : 4.3/5 (511 download)
Download or read book Bayesian Regression Modeling with INLA written by Xiaofeng Wang and published by CRC Press. This book was released on 2018-01-29 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: INLA stands for Integrated Nested Laplace Approximations, which is a new method for fitting a broad class of Bayesian regression models. No samples of the posterior marginal distributions need to be drawn using INLA, so it is a computationally convenient alternative to Markov chain Monte Carlo (MCMC), the standard tool for Bayesian inference. Bayesian Regression Modeling with INLA covers a wide range of modern regression models and focuses on the INLA technique for building Bayesian models using real-world data and assessing their validity. A key theme throughout the book is that it makes sense to demonstrate the interplay of theory and practice with reproducible studies. Complete R commands are provided for each example, and a supporting website holds all of the data described in the book. An R package including the data and additional functions in the book is available to download. The book is aimed at readers who have a basic knowledge of statistical theory and Bayesian methodology. It gets readers up to date on the latest in Bayesian inference using INLA and prepares them for sophisticated, real-world work. Xiaofeng Wang is Professor of Medicine and Biostatistics at the Cleveland Clinic Lerner College of Medicine of Case Western Reserve University and a Full Staff in the Department of Quantitative Health Sciences at Cleveland Clinic. Yu Ryan Yue is Associate Professor of Statistics in the Paul H. Chook Department of Information Systems and Statistics at Baruch College, The City University of New York. Julian J. Faraway is Professor of Statistics in the Department of Mathematical Sciences at the University of Bath.
Author : Pierre-Jean Laurent
Publisher : Academic Press
ISBN 13 : 1483263878
Total Pages : 535 pages
Book Rating : 4.4/5 (832 download)
Download or read book Curves and Surfaces written by Pierre-Jean Laurent and published by Academic Press. This book was released on 2014-05-12 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: Curves and Surfaces provides information pertinent to the fundamental aspects of approximation theory with emphasis on approximation of images, surface compression, wavelets, and tomography. This book covers a variety of topics, including error estimates for multiquadratic interpolation, spline manifolds, and vector spline approximation. Organized into 77 chapters, this book begins with an overview of the method, based on a local Taylor expansion of the final curve, for computing the parameter values. This text then presents a vector approximation based on general spline function theory. Other chapters consider a nonparametric technique for estimating under random censorship the amplitude of a change point in change point hazard models. This book discusses as well the algorithm for ray tracing rational parametric surfaces based on inversion and implicitization. The final chapter deals with the results concerning the norm of the interpolation operator and error estimates for a square domain. This book is a valuable resource for mathematicians.
Author : Atanu Biswas
Publisher : John Wiley & Sons
ISBN 13 : 0470181192
Total Pages : 623 pages
Book Rating : 4.4/5 (71 download)
Download or read book Statistical Advances in the Biomedical Sciences written by Atanu Biswas and published by John Wiley & Sons. This book was released on 2007-12-14 with total page 623 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Most Comprehensive and Cutting-Edge Guide to Statistical Applications in Biomedical Research With the increasing use of biotechnology in medical research and the sophisticated advances in computing, it has become essential for practitioners in the biomedical sciences to be fully educated on the role statistics plays in ensuring the accurate analysis of research findings. Statistical Advances in the Biomedical Sciences explores the growing value of statistical knowledge in the management and comprehension of medical research and, more specifically, provides an accessible introduction to the contemporary methodologies used to understand complex problems in the four major areas of modern-day biomedical science: clinical trials, epidemiology, survival analysis, and bioinformatics. Composed of contributions from eminent researchers in the field, this volume discusses the application of statistical techniques to various aspects of modern medical research and illustrates how these methods ultimately prove to be an indispensable part of proper data collection and analysis. A structural uniformity is maintained across all chapters, each beginning with an introduction that discusses general concepts and the biomedical problem under focus and is followed by specific details on the associated methods, algorithms, and applications. In addition, each chapter provides a summary of the main ideas and offers a concluding remarks section that presents novel ideas, approaches, and challenges for future research. Complete with detailed references and insight on the future directions of biomedical research, Statistical Advances in the Biomedical Sciences provides vital statistical guidance to practitioners in the biomedical sciences while also introducing statisticians to new, multidisciplinary frontiers of application. This text is an excellent reference for graduate- and PhD-level courses in various areas of biostatistics and the medical sciences and also serves as a valuable tool for medical researchers, statisticians, public health professionals, and biostatisticians.
Author : Wolfgang Härdle
Publisher : Springer Science & Business Media
ISBN 13 : 9783540207221
Total Pages : 340 pages
Book Rating : 4.2/5 (72 download)
Download or read book Nonparametric and Semiparametric Models written by Wolfgang Härdle and published by Springer Science & Business Media. This book was released on 2004-03-22 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: The statistical and mathematical principles of smoothing with a focus on applicable techniques are presented in this book. It naturally splits into two parts: The first part is intended for undergraduate students majoring in mathematics, statistics, econometrics or biometrics whereas the second part is intended to be used by master and PhD students or researchers. The material is easy to accomplish since the e-book character of the text gives a maximum of flexibility in learning (and teaching) intensity.
