Estimation Of Posterior Probabilities Using Multivariate Smoothing Splines And Generalized Cross Validation

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Estimation Of Posterior Probabilities Using Multivariate Smoothing Splines And Generalized Cross Validation

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Author : Miguel Agustin Villalobos
language : en
Publisher:
Release Date : 1983

Estimation Of Posterior Probabilities Using Multivariate Smoothing Splines And Generalized Cross Validation written by Miguel Agustin Villalobos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Probabilities categories.

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.

Topics In Multivariate Approximation

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Author : C. K. Chui
language : en
Publisher: Elsevier
Release Date : 2014-05-10

Topics In Multivariate Approximation written by C. K. Chui and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.

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.

Journal Of The American Statistical Association

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Author :
language : en
Publisher:
Release Date : 2006

Journal Of The American Statistical Association written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Statistics categories.

Scientific And Technical Aerospace Reports

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Author :
language : en
Publisher:
Release Date : 1984

Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Aeronautics categories.

Spline Models For Observational Data

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Author : Grace Wahba
language : en
Publisher: SIAM
Release Date : 1990-01-01

Spline Models For Observational Data written by Grace Wahba and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Mathematics categories.

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.

Smoothing Spline Estimation Of Functions With Discontinuities

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Author : Jyh-Jen Horng Shiau
language : en
Publisher:
Release Date : 1985

Smoothing Spline Estimation Of Functions With Discontinuities written by Jyh-Jen Horng Shiau and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.

Function Estimates

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Author : James Stephen Marron
language : en
Publisher: American Mathematical Soc.
Release Date : 1986

Function Estimates written by James Stephen Marron and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.

This volume collects together papers presented at the 1985 Conference in Function Estimation held at Humboldt State University. The papers focus especially on various types of spline estimations and convolution problems. The use of estimation and approximation methods as applied to geophysics, numerical analysis, and nonparametric statistics was a special feature of this conference.

Multivariate Statistical Modelling Based On Generalized Linear Models

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Author : Ludwig Fahrmeir
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Multivariate Statistical Modelling Based On Generalized Linear Models written by Ludwig Fahrmeir and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.

Since our first edition of this book, many developments in statistical mod elling based on generalized linear models have been published, and our primary aim is to bring the book up to date. Naturally, the choice of these recent developments reflects our own teaching and research interests. The new organization parallels that of the first edition. We try to motiv ate and illustrate concepts with examples using real data, and most data sets are available on http:/ fwww. stat. uni-muenchen. de/welcome_e. html, with a link to data archive. We could not treat all recent developments in the main text, and in such cases we point to references at the end of each chapter. Many changes will be found in several sections, especially with those connected to Bayesian concepts. For example, the treatment of marginal models in Chapter 3 is now current and state-of-the-art. The coverage of nonparametric and semiparametric generalized regression in Chapter 5 is completely rewritten with a shift of emphasis to linear bases, as well as new sections on local smoothing approaches and Bayesian inference. Chapter 6 now incorporates developments in parametric modelling of both time series and longitudinal data. Additionally, random effect models in Chapter 7 now cover nonparametric maximum likelihood and a new section on fully Bayesian approaches. The modifications and extensions in Chapter 8 reflect the rapid development in state space and hidden Markov models.

Technical Report

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Author : University of Wisconsin--Madison. Department of Statistics
language : en
Publisher:
Release Date : 1972

Technical Report written by University of Wisconsin--Madison. Department of Statistics and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with categories.

Inverse And Ill Posed Problems

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Author : Heinz W. Engl
language : en
Publisher: Elsevier
Release Date : 2014-05-10

Inverse And Ill Posed Problems written by Heinz W. Engl and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.

Inverse and Ill-Posed Problems is a collection of papers presented at a seminar of the same title held in Austria in June 1986. The papers discuss inverse problems in various disciplines; mathematical solutions of integral equations of the first kind; general considerations for ill-posed problems; and the various regularization methods for integral and operator equations of the first kind. Other papers deal with applications in tomography, inverse scattering, detection of radiation sources, optics, partial differential equations, and parameter estimation problems. One paper discusses three topics on ill-posed problems, namely, the imposition of specified types of discontinuities on solutions of ill-posed problems, the use of generalized cross validation as a data based termination rule for iterative methods, and also a parameter estimation problem in reservoir modeling. Another paper investigates a statistical method to determine the truncation level in Eigen function expansions and for Fredholm equations of the first kind where the data contains some errors. Another paper examines the use of singular function expansions in the inversion of severely ill-posed problems arising in confocal scanning microscopy, particle sizing, and velocimetry. The collection can benefit many mathematicians, students, and professor of calculus, statistics, and advanced mathematics.