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Multivariate Kernel Smoothing And Its Applications

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Multivariate Kernel Smoothing And Its Applications

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Author : José E. Chacón
language : en
Publisher: CRC Press
Release Date : 2018-05-08

Multivariate Kernel Smoothing And Its Applications written by José E. Chacón and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-08 with Mathematics categories.

Kernel smoothing has greatly evolved since its inception to become an essential methodology in the data science tool kit for the 21st century. Its widespread adoption is due to its fundamental role for multivariate exploratory data analysis, as well as the crucial role it plays in composite solutions to complex data challenges. Multivariate Kernel Smoothing and Its Applications offers a comprehensive overview of both aspects. It begins with a thorough exposition of the approaches to achieve the two basic goals of estimating probability density functions and their derivatives. The focus then turns to the applications of these approaches to more complex data analysis goals, many with a geometric/topological flavour, such as level set estimation, clustering (unsupervised learning), principal curves, and feature significance. Other topics, while not direct applications of density (derivative) estimation but sharing many commonalities with the previous settings, include classification (supervised learning), nearest neighbour estimation, and deconvolution for data observed with error. For a data scientist, each chapter contains illustrative Open data examples that are analysed by the most appropriate kernel smoothing method. The emphasis is always placed on an intuitive understanding of the data provided by the accompanying statistical visualisations. For a reader wishing to investigate further the details of their underlying statistical reasoning, a graduated exposition to a unified theoretical framework is provided. The algorithms for efficient software implementation are also discussed. José E. Chacón is an associate professor at the Department of Mathematics of the Universidad de Extremadura in Spain. Tarn Duong is a Senior Data Scientist for a start-up which provides short distance carpooling services in France. Both authors have made important contributions to kernel smoothing research over the last couple of decades.

Kernel Smoothing

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Author : Sucharita Ghosh
language : en
Publisher: John Wiley & Sons
Release Date : 2018-01-09

Kernel Smoothing written by Sucharita Ghosh 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 2018-01-09 with Mathematics categories.

Comprehensive theoretical overview of kernel smoothing methods with motivating examples Kernel smoothing is a flexible nonparametric curve estimation method that is applicable when parametric descriptions of the data are not sufficiently adequate. This book explores theory and methods of kernel smoothing in a variety of contexts, considering independent and correlated data e.g. with short-memory and long-memory correlations, as well as non-Gaussian data that are transformations of latent Gaussian processes. These types of data occur in many fields of research, e.g. the natural and the environmental sciences, and others. Nonparametric density estimation, nonparametric and semiparametric regression, trend and surface estimation in particular for time series and spatial data and other topics such as rapid change points, robustness etc. are introduced alongside a study of their theoretical properties and optimality issues, such as consistency and bandwidth selection. Addressing a variety of topics, Kernel Smoothing: Principles, Methods and Applications offers a user-friendly presentation of the mathematical content so that the reader can directly implement the formulas using any appropriate software. The overall aim of the book is to describe the methods and their theoretical backgrounds, while maintaining an analytically simple approach and including motivating examples—making it extremely useful in many sciences such as geophysics, climate research, forestry, ecology, and other natural and life sciences, as well as in finance, sociology, and engineering. A simple and analytical description of kernel smoothing methods in various contexts Presents the basics as well as new developments Includes simulated and real data examples Kernel Smoothing: Principles, Methods and Applications is a textbook for senior undergraduate and graduate students in statistics, as well as a reference book for applied statisticians and advanced researchers.

Kernel Smoothing

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Author : M.P. Wand
language : en
Publisher: CRC Press
Release Date : 1994-12-01

Kernel Smoothing written by M.P. Wand and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-12-01 with Mathematics categories.

Kernel smoothing refers to a general methodology for recovery of underlying structure in data sets. The basic principle is that local averaging or smoothing is performed with respect to a kernel function. This book provides uninitiated readers with a feeling for the principles, applications, and analysis of kernel smoothers. This is facilitated by the authors' focus on the simplest settings, namely density estimation and nonparametric regression. They pay particular attention to the problem of choosing the smoothing parameter of a kernel smoother, and also treat the multivariate case in detail. Kernal Smoothing is self-contained and assumes only a basic knowledge of statistics, calculus, and matrix algebra. It is an invaluable introduction to the main ideas of kernel estimation for students and researchers from other discipline and provides a comprehensive reference for those familiar with the topic.

Kernel Smoothing

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Author : M. P. Wand
language : en
Publisher: Springer
Release Date : 1995-01-01

Kernel Smoothing written by M. P. Wand and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-01 with Computers categories.

Multivariate Density Estimation

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Author : David W. Scott
language : en
Publisher: John Wiley & Sons
Release Date : 1992-08-31

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 1992-08-31 with Mathematics categories.

Representation and geometry of multivariate data; Nonparametric estimation criteria; Histograms: theory and practice; Frequency polygons; Averaged shifted histograms; Kernel density estimators; The curse of dimensionality and dimension reduction; Nonparametric regression and additive models; Other applications.

Kernel Smoothing In Matlab

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Author : Ivanka Horová
language : en
Publisher: World Scientific
Release Date : 2012-08-14

Kernel Smoothing In Matlab written by Ivanka Horová and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-14 with Mathematics categories.

Methods of kernel estimates represent one of the most effective nonparametric smoothing techniques. These methods are simple to understand and they possess very good statistical properties. This book provides a concise and comprehensive overview of statistical theory and in addition, emphasis is given to the implementation of presented methods in Matlab. All created programs are included in a special toolbox which is an integral part of the book. This toolbox contains many Matlab scripts useful for kernel smoothing of density, cumulative distribution function, regression function, hazard function, indices of quality and bivariate density. Specifically, methods for choosing a choice of the optimal bandwidth and a special procedure for simultaneous choice of the bandwidth, the kernel and its order are implemented. The toolbox is divided into six parts according to the chapters of the book. All scripts are included in a user interface and it is easy to manipulate with this interface. Each chapter of the book contains a detailed help for the related part of the toolbox too. This book is intended for newcomers to the field of smoothing techniques and would also be appropriate for a wide audience: advanced graduate, PhD students and researchers from both the statistical science and interface disciplines. Contents:IntroductionUnivariate Kernel Density EstimationKernel Estimation of a Distribution FunctionKernel Estimation and Reliability AssessmentKernel Estimation of a Hazard FunctionKernel Estimation of a Regression FunctionMultivariate Kernel Density Estimation Readership: Advanced graduate students, researchers in mathematics or statistics. Keywords:Kernel;Bandwidth;Density Estimate;Kernel Regression;Hazard FunctionKey Features:Toolbox in MatlabBrief overview of existing methodsDeveloping a new unifying bandwidth selection method

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 And Regression

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Author : Michael G. Schimek
language : en
Publisher: John Wiley & Sons
Release Date : 2013-05-29

Smoothing And Regression written by Michael G. Schimek 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 2013-05-29 with Mathematics categories.

A comprehensive introduction to a wide variety of univariate and multivariate smoothing techniques for regression Smoothing and Regression: Approaches, Computation, and Application bridges the many gaps that exist among competing univariate and multivariate smoothing techniques. It introduces, describes, and in some cases compares a large number of the latest and most advanced techniques for regression modeling. Unlike many other volumes on this topic, which are highly technical and specialized, this book discusses all methods in light of both computational efficiency and their applicability for real data analysis. Using examples of applications from the biosciences, environmental sciences, engineering, and economics, as well as medical research and marketing, this volume addresses the theory, computation, and application of each approach. A number of the techniques discussed, such as smoothing under shape restrictions or of dependent data, are presented for the first time in book form. Special features of this book include: * Comprehensive coverage of smoothing and regression with software hints and applications from a wide variety of disciplines * A unified, easy-to-follow format * Contributions from more than 25 leading researchers from around the world * More than 150 illustrations also covering new graphical techniques important for exploratory data analysis and visualization of high-dimensional problems * Extensive end-of-chapter references For professionals and aspiring professionals in statistics, applied mathematics, computer science, and econometrics, as well as for researchers in the applied and social sciences, Smoothing and Regression is a unique and important new resource destined to become one the most frequently consulted references in the field.

Nonparametric Econometrics

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Author : Qi Li
language : en
Publisher: Princeton University Press
Release Date : 2023-07-18

Nonparametric Econometrics written by Qi Li and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-18 with Business & Economics categories.

A comprehensive, up-to-date textbook on nonparametric methods for students and researchers Until now, students and researchers in nonparametric and semiparametric statistics and econometrics have had to turn to the latest journal articles to keep pace with these emerging methods of economic analysis. Nonparametric Econometrics fills a major gap by gathering together the most up-to-date theory and techniques and presenting them in a remarkably straightforward and accessible format. The empirical tests, data, and exercises included in this textbook help make it the ideal introduction for graduate students and an indispensable resource for researchers. Nonparametric and semiparametric methods have attracted a great deal of attention from statisticians in recent decades. While the majority of existing books on the subject operate from the presumption that the underlying data is strictly continuous in nature, more often than not social scientists deal with categorical data—nominal and ordinal—in applied settings. The conventional nonparametric approach to dealing with the presence of discrete variables is acknowledged to be unsatisfactory. This book is tailored to the needs of applied econometricians and social scientists. Qi Li and Jeffrey Racine emphasize nonparametric techniques suited to the rich array of data types—continuous, nominal, and ordinal—within one coherent framework. They also emphasize the properties of nonparametric estimators in the presence of potentially irrelevant variables. Nonparametric Econometrics covers all the material necessary to understand and apply nonparametric methods for real-world problems.

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 Kernel Smoothing And Its Applications

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