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.

Download or read book Handbook of Splines written by Gheorghe Micula and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to give a comprehensive introduction to the theory of spline functions, together with some applications to various fields, emphasizing the significance of the relationship between the general theory and its applications. At the same time, the goal of the book is also to provide new ma terial on spline function theory, as well as a fresh look at old results, being written for people interested in research, as well as for those who are interested in applications. The theory of spline functions and their applications is a relatively recent field of applied mathematics. In the last 50 years, spline function theory has undergone a won derful development with many new directions appearing during this time. This book has its origins in the wish to adequately describe this development from the notion of 'spline' introduced by 1. J. Schoenberg (1901-1990) in 1946, to the newest recent theories of 'spline wavelets' or 'spline fractals'. Isolated facts about the functions now called 'splines' can be found in the papers of L. Euler, A. Lebesgue, G. Birkhoff, J.

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 Hilbertian Kernels and Spline Functions written by M. Atteia and published by Elsevier. This book was released on 2014-06-28 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, which is an extensive study of Hilbertian approximation, the emphasis is placed on spline functions theory. The origin of the book was an effort to show that spline theory parallels Hilbertian Kernel theory, not only for splines derived from minimization of a quadratic functional but more generally for splines considered as piecewise functions type.Being as far as possible self-contained, the book may be used as a reference, with information about developments in linear approximation, convex optimization, mechanics and partial differential equations.

Download or read book Topics in Multivariate Approximation written by C. K. Chui and published by Elsevier. This book was released on 2014-05-10 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics in Multivariate Approximation contains the proceedings of an international workshop on multivariate approximation held at the University of Chile in Santiago, Chile, on December 15-19, 1986. Leading researchers in the field discussed several problem areas related to multivariate approximation and tackled topics ranging from multivariate splines and fitting of scattered data to tensor approximation methods and multivariate polynomial approximation. Numerical grid generation and finite element methods were also explored, along with constrained interpolation and smoothing. Comprised of 22 chapters, this book first describes the application of Boolean methods of approximation in combination with the theory of right invertible operators to bivariate Fourier expansions. The reader is then introduced to ill-posed problems in multivariate approximation; interpolation of scattered data by radial functions; and shape-preserving surface interpolation. Subsequent chapters focus on approximation by harmonic functions; numerical generation of nested series of general triangular grids; triangulation methods; and inequalities arising from best local approximations in rectangles. A bibliography of multivariate approximation concludes the book. This monograph will be of interest to mathematicians.

Download or read book Multivariate Approximation From Cagd To Wavelets Proceedings Of The International Workshop written by Kurt Jetter and published by World Scientific. This book was released on 1993-11-30 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: Fast Algorithms for Simultaneous Polynomial Approximation (G Baszenski & M Tasche)α-Spline of Smoothing for Correlated Errors in Dimension Two (M Bozzini & L Lenarduzzi)New Developments in the Theory of Radial Basis Function Interpolation (M D Buhmann)Realization of Neural Networks with One Hidden Layer (C K Chui & X Li)A General Method for Constrained Curves with Boundary Conditions (P Costantini)Sign-Regular and Totally Positive Matrices: An Algorithmic Approach (M Gasca & J M Peña)Some Results on Blossoming and Multivariate B-Splines (R Gormaz & P-J Laurent)Riesz Bounds in Scattered Data Interpolation and L2-Approximation (K Jetter)On Multivariate Hermite Polynomial Interpolation (A Le Méhauté)Quantitative Approximation Results for Sigma-Pi-Type Neural Network Operators (B Lenze)Local Interpolation Schemes — From Curves to Surfaces (D Levin)Some Results on Approximation by Smoothing Dm-Splines (M C L de Silanes) Readership: Applied mathematicians.

Download or read book Multidimensional Minimizing Splines written by R. Arcangéli and published by Springer Science & Business Media. This book was released on 2006-02-27 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is of interest to mathematicians, geologists, engineers and, in general, researchers and post graduate students involved in spline function theory, surface fitting problems or variational methods. From reviews: The book is well organized, and the English is very good. I recommend the book to researchers in approximation theory, and to anyone interested in bivariate data fitting." (L.L. Schumaker, Mathematical Reviews, 2005).

Download or read book Smoothing and Regression written by Michael G. Schimek and published by John Wiley & Sons. This book was released on 2013-05-29 with total page 682 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to a wide variety of univariate and multivariate smoothing techniques for regression Smoothing and Regression: Approaches, Computation, and Application bridges the many gaps that exist among competing univariate and multivariate smoothing techniques. It introduces, describes, and in some cases compares a large number of the latest and most advanced techniques for regression modeling. Unlike many other volumes on this topic, which are highly technical and specialized, this book discusses all methods in light of both computational efficiency and their applicability for real data analysis. Using examples of applications from the biosciences, environmental sciences, engineering, and economics, as well as medical research and marketing, this volume addresses the theory, computation, and application of each approach. A number of the techniques discussed, such as smoothing under shape restrictions or of dependent data, are presented for the first time in book form. Special features of this book include: * Comprehensive coverage of smoothing and regression with software hints and applications from a wide variety of disciplines * A unified, easy-to-follow format * Contributions from more than 25 leading researchers from around the world * More than 150 illustrations also covering new graphical techniques important for exploratory data analysis and visualization of high-dimensional problems * Extensive end-of-chapter references For professionals and aspiring professionals in statistics, applied mathematics, computer science, and econometrics, as well as for researchers in the applied and social sciences, Smoothing and Regression is a unique and important new resource destined to become one the most frequently consulted references in the field.

Download or read book Perspectives on Big Data Analysis written by S. Ejaz Ahmed and published by American Mathematical Society. This book was released on 2014-08-20 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the International Workshop on Perspectives on High-dimensional Data Analysis II, held May 30-June 1, 2012, at the Centre de Recherches Mathématiques, Université de Montréal, Montréal, Quebec, Canada. This book collates applications and methodological developments in high-dimensional statistics dealing with interesting and challenging problems concerning the analysis of complex, high-dimensional data with a focus on model selection and data reduction. The chapters contained in this book deal with submodel selection and parameter estimation for an array of interesting models. The book also presents some surprising results on high-dimensional data analysis, especially when signals cannot be effectively separated from the noise, it provides a critical assessment of penalty estimation when the model may not be sparse, and it suggests alternative estimation strategies. Readers can apply the suggested methodologies to a host of applications and also can extend these methodologies in a variety of directions. This volume conveys some of the surprises, puzzles and success stories in big data analysis and related fields. This book is co-published with the Centre de Recherches Mathématiques.

Download or read book SIAM Journal on Scientific and Statistical Computing written by Society for Industrial and Applied Mathematics and published by . This book was released on 1991 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Multivariate Approximation and Interpolation written by Werner Haussmann and published by . This book was released on 1990 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Smoothing Spline ANOVA Models written by Chong Gu and published by Springer. This book was released on 2015-06-25 with total page 0 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 Scientific and Technical Aerospace Reports written by and published by . This book was released on 1984 with total page 1278 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Technical Report written by University of Wisconsin--Madison. Department of Statistics and published by . This book was released on 1972 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book High Dimensional Probability written by Evarist Giné and published by IMS. This book was released on 2006 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Nonparametric Regression and Spline Smoothing written by Randall L. Eubank and published by CRC Press. This book was released on 1999-02-09 with total page 359 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 co

Download or read book Estimation of Posterior Probabilities Using Multivariate Smoothing Splines and Generalized Cross validation written by Miguel Agustin Villalobos and published by . This book was released on 1983 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: A nonparametric estimate for the posterior probabilities in the classification problem using multivariate smoothing splines is proposed. This estimate presents a nonparametric alternative to logistic discrimination and to survival curve estimation. It is useful in exploring properties of the data and in presenting them in a way comprehensible to the layman. The estimate is obtained as the solution to a constrained minimization problem in a reproducing kernel Hilbert space. It is shown that under certain conditions an estimate exists and is unique.