Smoothing Splines

Author : Chong Gu
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 52,9 Mb
Release : 2002-01-08
Category : Mathematics
ISBN : 0387953531

Get Book

Smoothing Spline ANOVA Models by Chong Gu Pdf

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.

Author : Yuedong Wang
Publisher : CRC Press
Page : 380 pages
File Size : 49,8 Mb
Release : 2011-06-22
Category : Computers
ISBN : 9781420077568

Get Book

Smoothing Splines by Yuedong Wang Pdf

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
Page : 446 pages
File Size : 46,8 Mb
Release : 2013-01-26
Category : Mathematics
ISBN : 9781461453697

Get Book

Smoothing Spline ANOVA Models by Chong Gu Pdf

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 : Paul Dierckx
Publisher : Oxford University Press
Page : 308 pages
File Size : 45,7 Mb
Release : 1995
Category : Computers
ISBN : 019853440X

Get Book

Curve and Surface Fitting with Splines by Paul Dierckx Pdf

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.

Author : Garrett Fitzmaurice,Marie Davidian,Geert Verbeke,Geert Molenberghs
Publisher : CRC Press
Page : 633 pages
File Size : 55,6 Mb
Release : 2008-08-11
Category : Mathematics
ISBN : 9781420011579

Get Book

Longitudinal Data Analysis by Garrett Fitzmaurice,Marie Davidian,Geert Verbeke,Geert Molenberghs Pdf

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

Author : Gary D. Knott
Publisher : Springer Science & Business Media
Page : 247 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781461213208

Get Book

Interpolating Cubic Splines by Gary D. Knott Pdf

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.

Author : Randall L. Eubank
Publisher : CRC Press
Page : 368 pages
File Size : 48,6 Mb
Release : 1999-02-09
Category : Mathematics
ISBN : 0824793374

Get Book

Nonparametric Regression and Spline Smoothing, Second Edition by Randall L. Eubank Pdf

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.

Author : Paul H.C. Eilers,Brian D. Marx
Publisher : Cambridge University Press
Page : 213 pages
File Size : 50,6 Mb
Release : 2021-03-18
Category : Computers
ISBN : 9781108482950

Get Book

Practical Smoothing by Paul H.C. Eilers,Brian D. Marx Pdf

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

Author : Magnus Egerstedt,Clyde Martin
Publisher : Princeton University Press
Page : 232 pages
File Size : 51,9 Mb
Release : 2009-12-07
Category : Mathematics
ISBN : 9781400833870

Get Book

Control Theoretic Splines by Magnus Egerstedt,Clyde Martin Pdf

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.

Author : Gheorghe Micula,Sanda Micula
Publisher : Springer Science & Business Media
Page : 622 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401153386

Get Book

Handbook of Splines by Gheorghe Micula,Sanda Micula Pdf

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.

Author : Karen Sue Messer
Publisher : Unknown
Page : 226 pages
File Size : 44,8 Mb
Release : 1985
Category : Approximation theory
ISBN : UCSD:31822004310470

Get Book

Boundary Effects on Smoothing Splines by Karen Sue Messer Pdf

Author : Young Kinh-Nhue Truong,Muhammad Sarfraz
Publisher : BoD – Books on Demand
Page : 162 pages
File Size : 52,8 Mb
Release : 2018-06-06
Category : Computers
ISBN : 9781789232509

Get Book

Topics in Splines and Applications by Young Kinh-Nhue Truong,Muhammad Sarfraz Pdf

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 : Barry Richard Zuckerman
Publisher : Unknown
Page : 202 pages
File Size : 50,8 Mb
Release : 1987
Category : Electronic
ISBN : UCAL:C2930518

Get Book

Local Weighting Methods for Smoothing Splines by Barry Richard Zuckerman Pdf

Author : Mikis D. Stasinopoulos,Robert A. Rigby,Gillian Z. Heller,Vlasios Voudouris,Fernanda De Bastiani
Publisher : CRC Press
Page : 513 pages
File Size : 51,8 Mb
Release : 2017-04-21
Category : Mathematics
ISBN : 9781351980371

Get Book

Flexible Regression and Smoothing by Mikis D. Stasinopoulos,Robert A. Rigby,Gillian Z. Heller,Vlasios Voudouris,Fernanda De Bastiani Pdf

This book is about learning from data using the Generalized Additive Models for Location, Scale and Shape (GAMLSS). GAMLSS extends the Generalized Linear Models (GLMs) and Generalized Additive Models (GAMs) to accommodate large complex datasets, which are increasingly prevalent. In particular, the GAMLSS statistical framework enables flexible regression and smoothing models to be fitted to the data. The GAMLSS model assumes that the response variable has any parametric (continuous, discrete or mixed) distribution which might be heavy- or light-tailed, and positively or negatively skewed. In addition, all the parameters of the distribution (location, scale, shape) can be modelled as linear or smooth functions of explanatory variables. Key Features: Provides a broad overview of flexible regression and smoothing techniques to learn from data whilst also focusing on the practical application of methodology using GAMLSS software in R. Includes a comprehensive collection of real data examples, which reflect the range of problems addressed by GAMLSS models and provide a practical illustration of the process of using flexible GAMLSS models for statistical learning. R code integrated into the text for ease of understanding and replication. Supplemented by a website with code, data and extra materials. This book aims to help readers understand how to learn from data encountered in many fields. It will be useful for practitioners and researchers who wish to understand and use the GAMLSS models to learn from data and also for students who wish to learn GAMLSS through practical examples.

Author : E.L. Ortiz
Publisher : Elsevier
Page : 430 pages
File Size : 41,5 Mb
Release : 1987-02-01
Category : Mathematics
ISBN : 0080872441

Get Book

Numerical Approximation of Partial Differential Equations by E.L. Ortiz Pdf

This selection of papers is concerned with problems arising in the numerical solution of differential equations, with an emphasis on partial differential equations. There is a balance between theoretical studies of approximation processes, the analysis of specific numerical techniques and the discussion of their application to concrete problems relevant to engineering and science. Special consideration has been given to innovative numerical techniques and to the treatment of three-dimensional and singular problems. These topics are discussed in several of the invited papers. The contributed papers are divided into five parts: techniques of approximation theory which are basic to the numerical treatment of differential equations; numerical techniques based on discrete processes; innovative methods based on polynomial and rational approximation; variational inequalities, conformal transformation and asymptotic techniques; and applications of differential equations to problems in science and engineering.