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.
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 Multivariate Statistical Modelling Based on Generalized Linear Models written by Ludwig Fahrmeir and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is aimed at applied statisticians, graduate students of statistics, and students and researchers with a strong interest in statistics and data analysis. This second edition is extensively revised, especially those sections relating with Bayesian concepts.
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 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 Technical Report written by University of Wisconsin--Madison. Department of Statistics and published by . This book was released on 1972 with total page 774 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Function Estimates written by James Stephen Marron and published by American Mathematical Soc.. This book was released on 1986 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Journal of the American Statistical Association written by and published by . This book was released on 2008 with total page 1788 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Smoothing Noisy Data with Multidimensional Splines and Generalized Cross validation written by James George Wendelberger and published by . This book was released on 1982 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Inverse and Ill Posed Problems written by Heinz W. Engl and published by Elsevier. This book was released on 2014-05-10 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Smoothing Spline Estimation of Functions with Discontinuities written by Jyh-Jen Horng Shiau and published by . This book was released on 1985 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book NASA Conference Publication written by and published by . This book was released on 1984 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 OSU Statistics Technical Report written by Ohio State University. Department of Statistics and published by . This book was released on 1995 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Statistics an Appraisal written by Herbert Aron David and published by Wiley-Blackwell. This book was released on 1984 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Global Scale Atmospheric Processes Research Program Review written by Barbara A. Worley and published by . This book was released on 1984 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bulletin Institute of Mathematical Statistics written by Institute of Mathematical Statistics and published by . This book was released on 1991 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt:
