Multivariate Density Estimation
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Multivariate Density Estimation
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Author : David W. Scott
language : en
Publisher: John Wiley & Sons
Release Date : 2015-03-12
Multivariate Density Estimation written by David W. Scott and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-12 with Mathematics categories.
Clarifies modern data analysis through nonparametric density estimation for a complete working knowledge of the theory and methods Featuring a thoroughly revised presentation, Multivariate Density Estimation: Theory, Practice, and Visualization, Second Edition maintains an intuitive approach to the underlying methodology and supporting theory of density estimation. Including new material and updated research in each chapter, the Second Edition presents additional clarification of theoretical opportunities, new algorithms, and up-to-date coverage of the unique challenges presented in the field of data analysis. The new edition focuses on the various density estimation techniques and methods that can be used in the field of big data. Defining optimal nonparametric estimators, the Second Edition demonstrates the density estimation tools to use when dealing with various multivariate structures in univariate, bivariate, trivariate, and quadrivariate data analysis. Continuing to illustrate the major concepts in the context of the classical histogram, Multivariate Density Estimation: Theory, Practice, and Visualization, Second Edition also features: Over 150 updated figures to clarify theoretical results and to show analyses of real data sets An updated presentation of graphic visualization using computer software such as R A clear discussion of selections of important research during the past decade, including mixture estimation, robust parametric modeling algorithms, and clustering More than 130 problems to help readers reinforce the main concepts and ideas presented Boxed theorems and results allowing easy identification of crucial ideas Figures in color in the digital versions of the book A website with related data sets Multivariate Density Estimation: Theory, Practice, and Visualization, Second Edition is an ideal reference for theoretical and applied statisticians, practicing engineers, as well as readers interested in the theoretical aspects of nonparametric estimation and the application of these methods to multivariate data. The Second Edition is also useful as a textbook for introductory courses in kernel statistics, smoothing, advanced computational statistics, and general forms of statistical distributions.
Multivariate Density Estimation
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Author :
language : en
Publisher:
Release Date : 2007
Multivariate Density Estimation written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
Smoothing Of Multivariate Data
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Author : Jussi Sakari Klemelä
language : en
Publisher: John Wiley & Sons
Release Date : 2009-09-04
Smoothing Of Multivariate Data written by Jussi Sakari Klemelä and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-04 with Mathematics categories.
An applied treatment of the key methods and state-of-the-art tools for visualizing and understanding statistical data Smoothing of Multivariate Data provides an illustrative and hands-on approach to the multivariate aspects of density estimation, emphasizing the use of visualization tools. Rather than outlining the theoretical concepts of classification and regression, this book focuses on the procedures for estimating a multivariate distribution via smoothing. The author first provides an introduction to various visualization tools that can be used to construct representations of multivariate functions, sets, data, and scales of multivariate density estimates. Next, readers are presented with an extensive review of the basic mathematical tools that are needed to asymptotically analyze the behavior of multivariate density estimators, with coverage of density classes, lower bounds, empirical processes, and manipulation of density estimates. The book concludes with an extensive toolbox of multivariate density estimators, including anisotropic kernel estimators, minimization estimators, multivariate adaptive histograms, and wavelet estimators. A completely interactive experience is encouraged, as all examples and figurescan be easily replicated using the R software package, and every chapter concludes with numerous exercises that allow readers to test their understanding of the presented techniques. The R software is freely available on the book's related Web site along with "Code" sections for each chapter that provide short instructions for working in the R environment. Combining mathematical analysis with practical implementations, Smoothing of Multivariate Data is an excellent book for courses in multivariate analysis, data analysis, and nonparametric statistics at the upper-undergraduate and graduatelevels. It also serves as a valuable reference for practitioners and researchers in the fields of statistics, computer science, economics, and engineering.
Smoothing Methods In Statistics
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Author : Jeffrey S. Simonoff
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Smoothing Methods In Statistics written by Jeffrey S. Simonoff 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 2012-12-06 with Mathematics categories.
The existence of high speed, inexpensive computing has made it easy to look at data in ways that were once impossible. Where once a data analyst was forced to make restrictive assumptions before beginning, the power of the computer now allows great freedom in deciding where an analysis should go. One area that has benefited greatly from this new freedom is that of non parametric density, distribution, and regression function estimation, or what are generally called smoothing methods. Most people are familiar with some smoothing methods (such as the histogram) but are unlikely to know about more recent developments that could be useful to them. If a group of experts on statistical smoothing methods are put in a room, two things are likely to happen. First, they will agree that data analysts seriously underappreciate smoothing methods. Smoothing meth ods use computing power to give analysts the ability to highlight unusual structure very effectively, by taking advantage of people's abilities to draw conclusions from well-designed graphics. Data analysts should take advan tage of this, they will argue.
Density Estimation For Statistics And Data Analysis
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Author : Bernard. W. Silverman
language : en
Publisher: Routledge
Release Date : 2018-02-19
Density Estimation For Statistics And Data Analysis written by Bernard. W. Silverman and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-19 with Mathematics categories.
Although there has been a surge of interest in density estimation in recent years, much of the published research has been concerned with purely technical matters with insufficient emphasis given to the technique's practical value. Furthermore, the subject has been rather inaccessible to the general statistician. The account presented in this book places emphasis on topics of methodological importance, in the hope that this will facilitate broader practical application of density estimation and also encourage research into relevant theoretical work. The book also provides an introduction to the subject for those with general interests in statistics. The important role of density estimation as a graphical technique is reflected by the inclusion of more than 50 graphs and figures throughout the text. Several contexts in which density estimation can be used are discussed, including the exploration and presentation of data, nonparametric discriminant analysis, cluster analysis, simulation and the bootstrap, bump hunting, projection pursuit, and the estimation of hazard rates and other quantities that depend on the density. This book includes general survey of methods available for density estimation. The Kernel method, both for univariate and multivariate data, is discussed in detail, with particular emphasis on ways of deciding how much to smooth and on computation aspects. Attention is also given to adaptive methods, which smooth to a greater degree in the tails of the distribution, and to methods based on the idea of penalized likelihood.
Multivariate Density Estimation
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Author : Jan Ćwik
language : en
Publisher:
Release Date : 1995
Multivariate Density Estimation written by Jan Ćwik and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.
Nonparametric Kernel Density Estimation And Its Computational Aspects
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Author : Artur Gramacki
language : en
Publisher: Springer
Release Date : 2017-12-21
Nonparametric Kernel Density Estimation And Its Computational Aspects written by Artur Gramacki and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-21 with Technology & Engineering categories.
This book describes computational problems related to kernel density estimation (KDE) – one of the most important and widely used data smoothing techniques. A very detailed description of novel FFT-based algorithms for both KDE computations and bandwidth selection are presented. The theory of KDE appears to have matured and is now well developed and understood. However, there is not much progress observed in terms of performance improvements. This book is an attempt to remedy this. The book primarily addresses researchers and advanced graduate or postgraduate students who are interested in KDE and its computational aspects. The book contains both some background and much more sophisticated material, hence also more experienced researchers in the KDE area may find it interesting. The presented material is richly illustrated with many numerical examples using both artificial and real datasets. Also, a number of practical applications related to KDE are presented.
Combinatorial Methods In Density Estimation
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Author : Luc Devroye
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Combinatorial Methods In Density Estimation written by Luc Devroye 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 2012-12-06 with Mathematics categories.
Density estimation has evolved enormously since the days of bar plots and histograms, but researchers and users are still struggling with the problem of the selection of the bin widths. This text explores a new paradigm for the data-based or automatic selection of the free parameters of density estimates in general so that the expected error is within a given constant multiple of the best possible error. The paradigm can be used in nearly all density estimates and for most model selection problems, both parametric and nonparametric. It is the first book on this topic. The text is intended for first-year graduate students in statistics and learning theory, and offers a host of opportunities for further research and thesis topics. Each chapter corresponds roughly to one lecture, and is supplemented with many classroom exercises. A one year course in probability theory at the level of Feller's Volume 1 should be more than adequate preparation. Gabor Lugosi is Professor at Universitat Pompeu Fabra in Barcelona, and Luc Debroye is Professor at McGill University in Montreal. In 1996, the authors, together with Lászlo Györfi, published the successful text, A Probabilistic Theory of Pattern Recognition with Springer-Verlag. Both authors have made many contributions in the area of nonparametric estimation.
Multivariate Density Estimation By Neural Networks
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Author : Dewi Peerlings
language : en
Publisher:
Release Date : 2021
Multivariate Density Estimation By Neural Networks written by Dewi Peerlings and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
Model Based Clustering Classification And Density Estimation Using Mclust In R
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Author : Luca Scrucca
language : en
Publisher: CRC Press
Release Date : 2023-04-20
Model Based Clustering Classification And Density Estimation Using Mclust In R written by Luca Scrucca and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-20 with Mathematics categories.
Model-based clustering and classification methods provide a systematic statistical approach to clustering, classification, and density estimation via mixture modeling. The model-based framework allows the problems of choosing or developing an appropriate clustering or classification method to be understood within the context of statistical modeling. The mclust package for the statistical environment R is a widely adopted platform implementing these model-based strategies. The package includes both summary and visual functionality, complementing procedures for estimating and choosing models. Key features of the book: An introduction to the model-based approach and the mclust R package A detailed description of mclust and the underlying modeling strategies An extensive set of examples, color plots, and figures along with the R code for reproducing them Supported by a companion website, including the R code to reproduce the examples and figures presented in the book, errata, and other supplementary material Model-Based Clustering, Classification, and Density Estimation Using mclust in R is accessible to quantitatively trained students and researchers with a basic understanding of statistical methods, including inference and computing. In addition to serving as a reference manual for mclust, the book will be particularly useful to those wishing to employ these model-based techniques in research or applications in statistics, data science, clinical research, social science, and many other disciplines.