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 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 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 user guide presents a popular smoothing tool with practical applications in machine learning, engineering, and statistics.

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 Smoothing Spline ANOVA Models written by Chong Gu and published by Springer Science & Business Media. This book was released on 2002-01-08 with total page 312 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 2013-03-09 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 Interpolating Cubic Splines written by Gary D. Knott and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: A spline is a thin flexible strip composed of a material such as bamboo or steel that can be bent to pass through or near given points in the plane, or in 3-space in a smooth manner. Mechanical engineers and drafting specialists find such (physical) splines useful in designing and in drawing plans for a wide variety of objects, such as for hulls of boats or for the bodies of automobiles where smooth curves need to be specified. These days, physi cal splines are largely replaced by computer software that can compute the desired curves (with appropriate encouragment). The same mathematical ideas used for computing "spline" curves can be extended to allow us to compute "spline" surfaces. The application ofthese mathematical ideas is rather widespread. Spline functions are central to computer graphics disciplines. Spline curves and surfaces are used in computer graphics renderings for both real and imagi nary objects. Computer-aided-design (CAD) systems depend on algorithms for computing spline functions, and splines are used in numerical analysis and statistics. Thus the construction of movies and computer games trav els side-by-side with the art of automobile design, sail construction, and architecture; and statisticians and applied mathematicians use splines as everyday computational tools, often divorced from graphic images.

Download or read book Curve and Surface Fitting with Splines written by Paul Dierckx and published by Oxford University Press. This book was released on 1995 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fitting of a curve or surface through a set of observational data is a very frequent problem in different disciplines (mathematics, engineering, medicine, ...) with many interesting applications. This book describes the algorithms and mathematical fundamentals of a widely used software package for data fitting with (tensor product) splines. As such it gives a survey of possibilities and benefits but also of the problems to cope with when approximating with this popular type of function. In particular it is demonstrated in detail how the properties of B-splines can be fully exploited for improving the computational efficiency and for incorporating different boundary or shape preserving constraints. Special attention is also paid to strategies for an automatic and adaptive knot selection with intent to obtain serious data reductions. The practical use of the smoothing software is illustrated with many examples, academic as well as taken from real life.

Download or read book Artificial Neural Nets and Genetic Algorithms written by Andrej Dobnikar and published by Springer Science & Business Media. This book was released on 1999-07-15 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the contents: Neural networks – theory and applications: NNs (= neural networks) classifier on continuous data domains– quantum associative memory – a new class of neuron-like discrete filters to image processing – modular NNs for improving generalisation properties – presynaptic inhibition modelling for image processing application – NN recognition system for a curvature primal sketch – NN based nonlinear temporal-spatial noise rejection system – relaxation rate for improving Hopfield network – Oja's NN and influence of the learning gain on its dynamics Genetic algorithms – theory and applications: transposition: a biological-inspired mechanism to use with GAs (= genetic algorithms) – GA for decision tree induction – optimising decision classifications using GAs – scheduling tasks with intertask communication onto multiprocessors by GAs – design of robust networks with GA – effect of degenerate coding on GAs – multiple traffic signal control using a GA – evolving musical harmonisation – niched-penalty approach for constraint handling in GAs – GA with dynamic population size – GA with dynamic niche clustering for multimodal function optimisation Soft computing and uncertainty: self-adaptation of evolutionary constructed decision trees by information spreading – evolutionary programming of near optimal NNs

Download or read book Control Theoretic Splines written by Magnus Egerstedt and published by Princeton University Press. This book was released on 2009-12-07 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Splines, both interpolatory and smoothing, have a long and rich history that has largely been application driven. This book unifies these constructions in a comprehensive and accessible way, drawing from the latest methods and applications to show how they arise naturally in the theory of linear control systems. Magnus Egerstedt and Clyde Martin are leading innovators in the use of control theoretic splines to bring together many diverse applications within a common framework. In this book, they begin with a series of problems ranging from path planning to statistics to approximation. Using the tools of optimization over vector spaces, Egerstedt and Martin demonstrate how all of these problems are part of the same general mathematical framework, and how they are all, to a certain degree, a consequence of the optimization problem of finding the shortest distance from a point to an affine subspace in a Hilbert space. They cover periodic splines, monotone splines, and splines with inequality constraints, and explain how any finite number of linear constraints can be added. This book reveals how the many natural connections between control theory, numerical analysis, and statistics can be used to generate powerful mathematical and analytical tools. This book is an excellent resource for students and professionals in control theory, robotics, engineering, computer graphics, econometrics, and any area that requires the construction of curves based on sets of raw data.

Download or read book Variational Theory of Splines written by Anatoly Yu. Bezhaev and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a systematic description of the variational theory of splines in Hilbert spaces. All central aspects are discussed in the general form: existence, uniqueness, characterization via reproducing mappings and kernels, convergence, error estimations, vector and tensor hybrids in splines, dimensional reducing (traces of splines onto manifolds), etc. All considerations are illustrated by practical examples. In every case the numerical algorithms for the construction of splines are demonstrated.

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.

Download or read book A Practical Guide to Splines written by Carl de Boor and published by Springer. This book was released on 2001-12-01 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the author’s experience with calculations involving polynomial splines, presenting those parts of the theory especially useful in calculations and stressing the representation of splines as weighted sums of B-splines. The B-spline theory is developed directly from the recurrence relations without recourse to divided differences. This reprint includes redrawn figures, and most formal statements are accompanied by proofs.

Download or read book Generalized Additive Models written by T.J. Hastie and published by Routledge. This book was released on 2017-10-19 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes an array of power tools for data analysis that are based on nonparametric regression and smoothing techniques. These methods relax the linear assumption of many standard models and allow analysts to uncover structure in the data that might otherwise have been missed. While McCullagh and Nelder's Generalized Linear Models shows how to extend the usual linear methodology to cover analysis of a range of data types, Generalized Additive Models enhances this methodology even further by incorporating the flexibility of nonparametric regression. Clear prose, exercises in each chapter, and case studies enhance this popular text.

Download or read book Longitudinal Data Analysis written by Garrett Fitzmaurice and published by CRC Press. This book was released on 2008-08-11 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although many books currently available describe statistical models and methods for analyzing longitudinal data, they do not highlight connections between various research threads in the statistical literature. Responding to this void, Longitudinal Data Analysis provides a clear, comprehensive, and unified overview of state-of-the-art theory

Download or read book Nonparametric Regression and Generalized Linear Models written by P.J. Green and published by CRC Press. This book was released on 1993-05-01 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonparametric Regression and Generalized Linear Models focuses on the roughness penalty method of nonparametric smoothing and shows how this technique provides a unifying approach to a wide range of smoothing problems. The emphasis is methodological rather than theoretical, and the authors concentrate on statistical and computation issues. Real data examples are used to illustrate the various methods and to compare them with standard parametric approaches. 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.

Download or read book Perspectives in Mathematical System Theory Control and Signal Processing written by Jan C. Willems and published by Springer. This book was released on 2010-03-10 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift, published on the occasion of the sixtieth birthday of Yutaka - mamoto (‘YY’ as he is occasionally casually referred to), contains a collection of articles by friends, colleagues, and former Ph.D. students of YY. They are a tribute to his friendship and his scienti?c vision and oeuvre, which has been a source of inspiration to the authors. Yutaka Yamamoto was born in Kyoto, Japan, on March 29, 1950. He studied applied mathematics and general engineering science at the Department of Applied Mathematics and Physics of Kyoto University, obtaining the B.S. and M.Sc. degrees in 1972 and 1974. His M.Sc. work was done under the supervision of Professor Yoshikazu Sawaragi. In 1974, he went to the Center for Mathematical System T- ory of the University of Florida in Gainesville. He obtained the M.Sc. and Ph.D. degrees, both in Mathematics, in 1976 and 1978, under the direction of Professor Rudolf Kalman.