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A Uniform Central Limit Theorem And Efficiency For Deconvolution Estimators
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Book Synopsis Mathematical Foundations of Infinite-Dimensional Statistical Models by : Evarist Giné
Download or read book Mathematical Foundations of Infinite-Dimensional Statistical Models written by Evarist Giné and published by Cambridge University Press. This book was released on 2021-03-25 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: In nonparametric and high-dimensional statistical models, the classical Gauss–Fisher–Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades. This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces. The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, approximation and wavelet theory, and the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is presented within the minimax paradigm of decision theory. This includes the basic theory of convolution kernel and projection estimation, but also Bayesian nonparametrics and nonparametric maximum likelihood estimation. In a final chapter the theory of adaptive inference in nonparametric models is developed, including Lepski's method, wavelet thresholding, and adaptive inference for self-similar functions. Winner of the 2017 PROSE Award for Mathematics.
Book Synopsis Current Index to Statistics, Applications, Methods and Theory by :
Download or read book Current Index to Statistics, Applications, Methods and Theory written by and published by . This book was released on 1999 with total page 948 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Current Index to Statistics (CIS) is a bibliographic index of publications in statistics, probability, and related fields.
Book Synopsis Nonparametric Curve Estimation by : Sam Efromovich
Download or read book Nonparametric Curve Estimation written by Sam Efromovich and published by Springer Science & Business Media. This book was released on 2008-01-19 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a systematic, comprehensive, and unified account of modern nonparametric statistics of density estimation, nonparametric regression, filtering signals, and time series analysis. The companion software package, available over the Internet, brings all of the discussed topics into the realm of interactive research. Virtually every claim and development mentioned in the book is illustrated with graphs which are available for the reader to reproduce and modify, making the material fully transparent and allowing for complete interactivity.
Book Synopsis Empirical Bayes Forecasts of One Time Series Using Many Predictors by : Thomas Knox
Download or read book Empirical Bayes Forecasts of One Time Series Using Many Predictors written by Thomas Knox and published by . This book was released on 2001 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider both frequentist and empirical Bayes forecasts of a single time series using a linear model with T observations and K orthonormal predictors. The frequentist formulation considers estimators that are equivariant under permutations (reorderings) of the regressors. The empirical Bayes formulation (both parametric and nonparametric) treats the coefficients as i.i.d. and estimates their prior. Asymptotically, when K is proportional to T the empirical Bayes estimator is shown to be: (i) optimal in Robbins' (1955, 1964) sense; (ii) the minimum risk equivariant estimator; and (iii) minimax in both the frequentist and Bayesian problems over a class of nonGaussian error distributions. Also, the asymptotic frequentist risk of the minimum risk equivariant estimator is shown to equal the Bayes risk of the (infeasible subjectivist) Bayes estimator in the Gaussian case, where the 'prior' is the weak limit of the empirical cdf of the true parameter values. Monte Carlo results are encouraging. The new estimators are used to forecast monthly postwar U.S. macroeconomic time series using the first 151 principal components from a large panel of predictors.
Book Synopsis Asymptotic Theory of Statistics and Probability by : Anirban DasGupta
Download or read book Asymptotic Theory of Statistics and Probability written by Anirban DasGupta and published by Springer Science & Business Media. This book was released on 2008-03-07 with total page 726 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book delivers an encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. The book is unique in its detailed coverage of fundamental topics. It is written in an extremely lucid style, with an emphasis on the conceptual discussion of the importance of a problem and the impact and relevance of the theorems. There is no other book in large sample theory that matches this book in coverage, exercises and examples, bibliography, and lucid conceptual discussion of issues and theorems.
Book Synopsis Gaussian and Non-Gaussian Linear Time Series and Random Fields by : Murray Rosenblatt
Download or read book Gaussian and Non-Gaussian Linear Time Series and Random Fields written by Murray Rosenblatt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principal focus here is on autoregressive moving average models and analogous random fields, with probabilistic and statistical questions also being discussed. The book contrasts Gaussian models with noncausal or noninvertible (nonminimum phase) non-Gaussian models and deals with problems of prediction and estimation. New results for nonminimum phase non-Gaussian processes are exposited and open questions are noted. Intended as a text for gradutes in statistics, mathematics, engineering, the natural sciences and economics, the only recommendation is an initial background in probability theory and statistics. Notes on background, history and open problems are given at the end of the book.
Book Synopsis The Fourier Transform and Its Applications by : Ronald Newbold Bracewell
Download or read book The Fourier Transform and Its Applications written by Ronald Newbold Bracewell and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1852 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Engineering Applications of Noncommutative Harmonic Analysis by : Gregory S. Chirikjian
Download or read book Engineering Applications of Noncommutative Harmonic Analysis written by Gregory S. Chirikjian and published by CRC Press. This book was released on 2021-02-25 with total page 697 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 2001. The classical Fourier transform is one of the most widely used mathematical tools in engineering. However, few engineers know that extensions of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. For those that may be aware of its potential value, there is still no place they can turn to for a clear presentation of the background they need to apply the concept to engineering problems. Engineering Applications of Noncommutative Harmonic Analysis brings this powerful tool to the engineering world. Written specifically for engineers and computer scientists, it offers a practical treatment of harmonic analysis in the context of particular Lie groups (rotation and Euclidean motion). It presents only a limited number of proofs, focusing instead on providing a review of the fundamental mathematical results unknown to most engineers and detailed discussions of specific applications. Advances in pure mathematics can lead to very tangible advances in engineering, but only if they are available and accessible to engineers. Engineering Applications of Noncommutative Harmonic Analysis provides the means for adding this valuable and effective technique to the engineer's toolbox.
Book Synopsis Cumulative Index to IMS Scientific Journals, 1960-1989 by : Bruce E. Trumbo
Download or read book Cumulative Index to IMS Scientific Journals, 1960-1989 written by Bruce E. Trumbo and published by . This book was released on 1990 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1990 with total page 976 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Book Synopsis High Dimensional Probability V by : David M. Mason
Download or read book High Dimensional Probability V written by David M. Mason and published by . This book was released on 2009 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Statistical Parametric Mapping: The Analysis of Functional Brain Images by : William D. Penny
Download or read book Statistical Parametric Mapping: The Analysis of Functional Brain Images written by William D. Penny and published by Elsevier. This book was released on 2011-04-28 with total page 689 pages. Available in PDF, EPUB and Kindle. Book excerpt: In an age where the amount of data collected from brain imaging is increasing constantly, it is of critical importance to analyse those data within an accepted framework to ensure proper integration and comparison of the information collected. This book describes the ideas and procedures that underlie the analysis of signals produced by the brain. The aim is to understand how the brain works, in terms of its functional architecture and dynamics. This book provides the background and methodology for the analysis of all types of brain imaging data, from functional magnetic resonance imaging to magnetoencephalography. Critically, Statistical Parametric Mapping provides a widely accepted conceptual framework which allows treatment of all these different modalities. This rests on an understanding of the brain's functional anatomy and the way that measured signals are caused experimentally. The book takes the reader from the basic concepts underlying the analysis of neuroimaging data to cutting edge approaches that would be difficult to find in any other source. Critically, the material is presented in an incremental way so that the reader can understand the precedents for each new development. This book will be particularly useful to neuroscientists engaged in any form of brain mapping; who have to contend with the real-world problems of data analysis and understanding the techniques they are using. It is primarily a scientific treatment and a didactic introduction to the analysis of brain imaging data. It can be used as both a textbook for students and scientists starting to use the techniques, as well as a reference for practicing neuroscientists. The book also serves as a companion to the software packages that have been developed for brain imaging data analysis. - An essential reference and companion for users of the SPM software - Provides a complete description of the concepts and procedures entailed by the analysis of brain images - Offers full didactic treatment of the basic mathematics behind the analysis of brain imaging data - Stands as a compendium of all the advances in neuroimaging data analysis over the past decade - Adopts an easy to understand and incremental approach that takes the reader from basic statistics to state of the art approaches such as Variational Bayes - Structured treatment of data analysis issues that links different modalities and models - Includes a series of appendices and tutorial-style chapters that makes even the most sophisticated approaches accessible
Book Synopsis Statistical Data Analysis by : Glen Cowan
Download or read book Statistical Data Analysis written by Glen Cowan and published by Oxford University Press. This book was released on 1998 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a guide to the practical application of statistics in data analysis as typically encountered in the physical sciences. It is primarily addressed at students and professionals who need to draw quantitative conclusions from experimental data. Although most of the examples are takenfrom particle physics, the material is presented in a sufficiently general way as to be useful to people from most branches of the physical sciences. The first part of the book describes the basic tools of data analysis: concepts of probability and random variables, Monte Carlo techniques,statistical tests, and methods of parameter estimation. The last three chapters are somewhat more specialized than those preceding, covering interval estimation, characteristic functions, and the problem of correcting distributions for the effects of measurement errors (unfolding).
Book Synopsis Fundamentals of Statistical Signal Processing by : Steven M. Kay
Download or read book Fundamentals of Statistical Signal Processing written by Steven M. Kay and published by Pearson Education. This book was released on 2013 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: "For those involved in the design and implementation of signal processing algorithms, this book strikes a balance between highly theoretical expositions and the more practical treatments, covering only those approaches necessary for obtaining an optimal estimator and analyzing its performance. Author Steven M. Kay discusses classical estimation followed by Bayesian estimation, and illustrates the theory with numerous pedagogical and real-world examples."--Cover, volume 1.
Book Synopsis Independent Component Analysis by : Aapo Hyvärinen
Download or read book Independent Component Analysis written by Aapo Hyvärinen and published by John Wiley & Sons. This book was released on 2004-04-05 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to ICA for students and practitioners Independent Component Analysis (ICA) is one of the most exciting new topics in fields such as neural networks, advanced statistics, and signal processing. This is the first book to provide a comprehensive introduction to this new technique complete with the fundamental mathematical background needed to understand and utilize it. It offers a general overview of the basics of ICA, important solutions and algorithms, and in-depth coverage of new applications in image processing, telecommunications, audio signal processing, and more. Independent Component Analysis is divided into four sections that cover: * General mathematical concepts utilized in the book * The basic ICA model and its solution * Various extensions of the basic ICA model * Real-world applications for ICA models Authors Hyvarinen, Karhunen, and Oja are well known for their contributions to the development of ICA and here cover all the relevant theory, new algorithms, and applications in various fields. Researchers, students, and practitioners from a variety of disciplines will find this accessible volume both helpful and informative.
Book Synopsis Bayesian Filtering and Smoothing by : Simo Särkkä
Download or read book Bayesian Filtering and Smoothing written by Simo Särkkä and published by Cambridge University Press. This book was released on 2013-09-05 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified Bayesian treatment of the state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models.
