Functional Data Analysis

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Functional Data Analysis

Author : James Ramsay
Publisher : Springer Science & Business Media
ISBN 13 : 147577107X
Total Pages : 317 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Functional Data Analysis by : James Ramsay

Download or read book Functional Data Analysis written by James Ramsay and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Included here are expressions in the functional domain of such classics as linear regression, principal components analysis, linear modelling, and canonical correlation analysis, as well as specifically functional techniques such as curve registration and principal differential analysis. Data arising in real applications are used throughout for both motivation and illustration, showing how functional approaches allow us to see new things, especially by exploiting the smoothness of the processes generating the data. The data sets exemplify the wide scope of functional data analysis; they are drawn from growth analysis, meteorology, biomechanics, equine science, economics, and medicine. The book presents novel statistical technology while keeping the mathematical level widely accessible. It is designed to appeal to students, applied data analysts, and to experienced researchers; and as such is of value both within statistics and across a broad spectrum of other fields. Much of the material appears here for the first time.

Introduction to Functional Data Analysis

Author : Piotr Kokoszka
Publisher : CRC Press
ISBN 13 : 1498746691
Total Pages : 311 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Introduction to Functional Data Analysis by : Piotr Kokoszka

Download or read book Introduction to Functional Data Analysis written by Piotr Kokoszka and published by CRC Press. This book was released on 2017-09-27 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Functional Data Analysis provides a concise textbook introduction to the field. It explains how to analyze functional data, both at exploratory and inferential levels. It also provides a systematic and accessible exposition of the methodology and the required mathematical framework. The book can be used as textbook for a semester-long course on FDA for advanced undergraduate or MS statistics majors, as well as for MS and PhD students in other disciplines, including applied mathematics, environmental science, public health, medical research, geophysical sciences and economics. It can also be used for self-study and as a reference for researchers in those fields who wish to acquire solid understanding of FDA methodology and practical guidance for its implementation. Each chapter contains plentiful examples of relevant R code and theoretical and data analytic problems. The material of the book can be roughly divided into four parts of approximately equal length: 1) basic concepts and techniques of FDA, 2) functional regression models, 3) sparse and dependent functional data, and 4) introduction to the Hilbert space framework of FDA. The book assumes advanced undergraduate background in calculus, linear algebra, distributional probability theory, foundations of statistical inference, and some familiarity with R programming. Other required statistics background is provided in scalar settings before the related functional concepts are developed. Most chapters end with references to more advanced research for those who wish to gain a more in-depth understanding of a specific topic.

Functional Data Analysis with R and MATLAB

Author : James Ramsay
Publisher : Springer Science & Business Media
ISBN 13 : 0387981853
Total Pages : 213 pages
Book Rating : 4.3/5 (879 download)

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Book Synopsis Functional Data Analysis with R and MATLAB by : James Ramsay

Download or read book Functional Data Analysis with R and MATLAB written by James Ramsay and published by Springer Science & Business Media. This book was released on 2009-06-29 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an application-oriented overview of functional analysis, with extended and accessible presentations of key concepts such as spline basis functions, data smoothing, curve registration, functional linear models and dynamic systems Functional data analysis is put to work in a wide a range of applications, so that new problems are likely to find close analogues in this book The code in R and Matlab in the book has been designed to permit easy modification to adapt to new data structures and research problems

Functional and Shape Data Analysis

Author : Anuj Srivastava
Publisher : Springer
ISBN 13 : 1493940201
Total Pages : 447 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Functional and Shape Data Analysis by : Anuj Srivastava

Download or read book Functional and Shape Data Analysis written by Anuj Srivastava and published by Springer. This book was released on 2016-10-03 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook for courses on function data analysis and shape data analysis describes how to define, compare, and mathematically represent shapes, with a focus on statistical modeling and inference. It is aimed at graduate students in analysis in statistics, engineering, applied mathematics, neuroscience, biology, bioinformatics, and other related areas. The interdisciplinary nature of the broad range of ideas covered—from introductory theory to algorithmic implementations and some statistical case studies—is meant to familiarize graduate students with an array of tools that are relevant in developing computational solutions for shape and related analyses. These tools, gleaned from geometry, algebra, statistics, and computational science, are traditionally scattered across different courses, departments, and disciplines; Functional and Shape Data Analysis offers a unified, comprehensive solution by integrating the registration problem into shape analysis, better preparing graduate students for handling future scientific challenges. Recently, a data-driven and application-oriented focus on shape analysis has been trending. This text offers a self-contained treatment of this new generation of methods in shape analysis of curves. Its main focus is shape analysis of functions and curves—in one, two, and higher dimensions—both closed and open. It develops elegant Riemannian frameworks that provide both quantification of shape differences and registration of curves at the same time. Additionally, these methods are used for statistically summarizing given curve data, performing dimension reduction, and modeling observed variability. It is recommended that the reader have a background in calculus, linear algebra, numerical analysis, and computation.

Applied Functional Data Analysis

Author : J.O. Ramsay
Publisher : Springer
ISBN 13 : 0387224653
Total Pages : 191 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Applied Functional Data Analysis by : J.O. Ramsay

Download or read book Applied Functional Data Analysis written by J.O. Ramsay and published by Springer. This book was released on 2007-11-23 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the ideas of functional data analysis by a number of case studies. The case studies are accessible to research workers in a wide range of disciplines. Every reader should gain not only a specific understanding of the methods of functional data analysis, but more importantly a general insight into the underlying patterns of thought. There is an associated web site with MATLABr and S?PLUSr implementations of the methods discussed.

Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators

Author : Tailen Hsing
Publisher : John Wiley & Sons
ISBN 13 : 0470016914
Total Pages : 362 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators by : Tailen Hsing

Download or read book Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators written by Tailen Hsing and published by John Wiley & Sons. This book was released on 2015-05-06 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA). The self–contained treatment of selected topics of functional analysis and operator theory includes reproducing kernel Hilbert spaces, singular value decomposition of compact operators on Hilbert spaces and perturbation theory for both self–adjoint and non self–adjoint operators. The probabilistic foundation for FDA is described from the perspective of random elements in Hilbert spaces as well as from the viewpoint of continuous time stochastic processes. Nonparametric estimation approaches including kernel and regularized smoothing are also introduced. These tools are then used to investigate the properties of estimators for the mean element, covariance operators, principal components, regression function and canonical correlations. A general treatment of canonical correlations in Hilbert spaces naturally leads to FDA formulations of factor analysis, regression, MANOVA and discriminant analysis. This book will provide a valuable reference for statisticians and other researchers interested in developing or understanding the mathematical aspects of FDA. It is also suitable for a graduate level special topics course.

Geostatistical Functional Data Analysis

Author : Jorge Mateu
Publisher : John Wiley & Sons
ISBN 13 : 1119387841
Total Pages : 452 pages
Book Rating : 4.1/5 (193 download)

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Book Synopsis Geostatistical Functional Data Analysis by : Jorge Mateu

Download or read book Geostatistical Functional Data Analysis written by Jorge Mateu and published by John Wiley & Sons. This book was released on 2021-12-13 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geostatistical Functional Data Analysis Explore the intersection between geostatistics and functional data analysis with this insightful new reference Geostatistical Functional Data Analysis presents a unified approach to modelling functional data when spatial and spatio-temporal correlations are present. The Editors link together the wide research areas of geostatistics and functional data analysis to provide the reader with a new area called geostatistical functional data analysis that will bring new insights and new open questions to researchers coming from both scientific fields. This book provides a complete and up-to-date account to deal with functional data that is spatially correlated, but also includes the most innovative developments in different open avenues in this field. Containing contributions from leading experts in the field, this practical guide provides readers with the necessary tools to employ and adapt classic statistical techniques to handle spatial regression. The book also includes: A thorough introduction to the spatial kriging methodology when working with functions A detailed exposition of more classical statistical techniques adapted to the functional case and extended to handle spatial correlations Practical discussions of ANOVA, regression, and clustering methods to explore spatial correlation in a collection of curves sampled in a region In-depth explorations of the similarities and differences between spatio-temporal data analysis and functional data analysis Aimed at mathematicians, statisticians, postgraduate students, and researchers involved in the analysis of functional and spatial data, Geostatistical Functional Data Analysis will also prove to be a powerful addition to the libraries of geoscientists, environmental scientists, and economists seeking insightful new knowledge and questions at the interface of geostatistics and functional data analysis.

Inference for Functional Data with Applications

Author : Lajos Horváth
Publisher : Springer Science & Business Media
ISBN 13 : 1461436559
Total Pages : 426 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Inference for Functional Data with Applications by : Lajos Horváth

Download or read book Inference for Functional Data with Applications written by Lajos Horváth and published by Springer Science & Business Media. This book was released on 2012-05-08 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recently developed statistical methods and theory required for the application of the tools of functional data analysis to problems arising in geosciences, finance, economics and biology. It is concerned with inference based on second order statistics, especially those related to the functional principal component analysis. While it covers inference for independent and identically distributed functional data, its distinguishing feature is an in depth coverage of dependent functional data structures, including functional time series and spatially indexed functions. Specific inferential problems studied include two sample inference, change point analysis, tests for dependence in data and model residuals and functional prediction. All procedures are described algorithmically, illustrated on simulated and real data sets, and supported by a complete asymptotic theory. The book can be read at two levels. Readers interested primarily in methodology will find detailed descriptions of the methods and examples of their application. Researchers interested also in mathematical foundations will find carefully developed theory. The organization of the chapters makes it easy for the reader to choose an appropriate focus. The book introduces the requisite, and frequently used, Hilbert space formalism in a systematic manner. This will be useful to graduate or advanced undergraduate students seeking a self-contained introduction to the subject. Advanced researchers will find novel asymptotic arguments.

Nonparametric Functional Data Analysis

Author : Frédéric Ferraty
Publisher : Springer Science & Business Media
ISBN 13 : 0387366202
Total Pages : 260 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Nonparametric Functional Data Analysis by : Frédéric Ferraty

Download or read book Nonparametric Functional Data Analysis written by Frédéric Ferraty and published by Springer Science & Business Media. This book was released on 2006-11-22 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern apparatuses allow us to collect samples of functional data, mainly curves but also images. On the other hand, nonparametric statistics produces useful tools for standard data exploration. This book links these two fields of modern statistics by explaining how functional data can be studied through parameter-free statistical ideas. At the same time it shows how functional data can be studied through parameter-free statistical ideas, and offers an original presentation of new nonparametric statistical methods for functional data analysis.

Analysis of Variance for Functional Data

Author : Jin-Ting Zhang
Publisher : CRC Press
ISBN 13 : 1439862745
Total Pages : 412 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Analysis of Variance for Functional Data by : Jin-Ting Zhang

Download or read book Analysis of Variance for Functional Data written by Jin-Ting Zhang and published by CRC Press. This book was released on 2013-06-18 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite research interest in functional data analysis in the last three decades, few books are available on the subject. Filling this gap, Analysis of Variance for Functional Data presents up-to-date hypothesis testing methods for functional data analysis. The book covers the reconstruction of functional observations, functional ANOVA, functional linear models with functional responses, ill-conditioned functional linear models, diagnostics of functional observations, heteroscedastic ANOVA for functional data, and testing equality of covariance functions. Although the methodologies presented are designed for curve data, they can be extended to surface data. Useful for statistical researchers and practitioners analyzing functional data, this self-contained book gives both a theoretical and applied treatment of functional data analysis supported by easy-to-use MATLAB® code. The author provides a number of simple methods for functional hypothesis testing. He discusses pointwise, L2-norm-based, F-type, and bootstrap tests. Assuming only basic knowledge of statistics, calculus, and matrix algebra, the book explains the key ideas at a relatively low technical level using real data examples. Each chapter also includes bibliographical notes and exercises. Real functional data sets from the text and MATLAB codes for analyzing the data examples are available for download from the author’s website.

Wavelets in Functional Data Analysis

Author : Pedro A. Morettin
Publisher : Springer
ISBN 13 : 3319596233
Total Pages : 106 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Wavelets in Functional Data Analysis by : Pedro A. Morettin

Download or read book Wavelets in Functional Data Analysis written by Pedro A. Morettin and published by Springer. This book was released on 2017-11-07 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelet-based procedures are key in many areas of statistics, applied mathematics, engineering, and science. This book presents wavelets in functional data analysis, offering a glimpse of problems in which they can be applied, including tumor analysis, functional magnetic resonance and meteorological data. Starting with the Haar wavelet, the authors explore myriad families of wavelets and how they can be used. High-dimensional data visualization (using Andrews' plots), wavelet shrinkage (a simple, yet powerful, procedure for nonparametric models) and a selection of estimation and testing techniques (including a discussion on Stein’s Paradox) make this a highly valuable resource for graduate students and experienced researchers alike.

Gaussian Process Regression Analysis for Functional Data

Author : Jian Qing Shi
Publisher : CRC Press
ISBN 13 : 1439837740
Total Pages : 214 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Gaussian Process Regression Analysis for Functional Data by : Jian Qing Shi

Download or read book Gaussian Process Regression Analysis for Functional Data written by Jian Qing Shi and published by CRC Press. This book was released on 2011-07-01 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gaussian Process Regression Analysis for Functional Data presents nonparametric statistical methods for functional regression analysis, specifically the methods based on a Gaussian process prior in a functional space. The authors focus on problems involving functional response variables and mixed covariates of functional and scalar variables.Coveri

Handbook of Functional MRI Data Analysis

Author : Russell A. Poldrack
Publisher : Cambridge University Press
ISBN 13 : 9781009481168
Total Pages : 0 pages
Book Rating : 4.4/5 (811 download)

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Book Synopsis Handbook of Functional MRI Data Analysis by : Russell A. Poldrack

Download or read book Handbook of Functional MRI Data Analysis written by Russell A. Poldrack and published by Cambridge University Press. This book was released on 2024-02-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional magnetic resonance imaging (fMRI) has become the most popular method for imaging brain function. Handbook for Functional MRI Data Analysis provides a comprehensive and practical introduction to the methods used for fMRI data analysis. Using minimal jargon, this book explains the concepts behind processing fMRI data, focusing on the techniques that are most commonly used in the field. This book provides background about the methods employed by common data analysis packages including FSL, SPM, and AFNI. Some of the newest cutting-edge techniques, including pattern classification analysis, connectivity modeling, and resting state network analysis, are also discussed. Readers of this book, whether newcomers to the field or experienced researchers, will obtain a deep and effective knowledge of how to employ fMRI analysis to ask scientific questions and become more sophisticated users of fMRI analysis software.

The Oxford Handbook of Functional Data Analysis

Author : Frédéric Ferraty
Publisher : OUP Oxford
ISBN 13 : 0199568448
Total Pages : 512 pages
Book Rating : 4.1/5 (995 download)

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Book Synopsis The Oxford Handbook of Functional Data Analysis by : Frédéric Ferraty

Download or read book The Oxford Handbook of Functional Data Analysis written by Frédéric Ferraty and published by OUP Oxford. This book was released on 2010-11-25 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Handbook aims to present a state of the art exploration of the high-tech field of functional data analysis, by gathering together most of major advances in this area.

The Statistical Analysis of Functional MRI Data

Author : Nicole Lazar
Publisher : Springer Science & Business Media
ISBN 13 : 0387781919
Total Pages : 302 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis The Statistical Analysis of Functional MRI Data by : Nicole Lazar

Download or read book The Statistical Analysis of Functional MRI Data written by Nicole Lazar and published by Springer Science & Business Media. This book was released on 2008-06-10 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of brain function is one of the most fascinating pursuits of m- ern science. Functional neuroimaging is an important component of much of the current research in cognitive, clinical, and social psychology. The exci- ment of studying the brain is recognized in both the popular press and the scienti?c community. In the pages of mainstream publications, including The New York Times and Wired, readers can learn about cutting-edge research into topics such as understanding how customers react to products and - vertisements (“If your brain has a ‘buy button,’ what pushes it?”, The New York Times,October19,2004),howviewersrespondtocampaignads(“Using M. R. I. ’s to see politics on the brain,” The New York Times, April 20, 2004; “This is your brain on Hillary: Political neuroscience hits new low,” Wired, November 12,2007),howmen and womenreactto sexualstimulation (“Brain scans arouse researchers,”Wired, April 19, 2004), distinguishing lies from the truth (“Duped,” The New Yorker, July 2, 2007; “Woman convicted of child abuse hopes fMRI can prove her innocence,” Wired, November 5, 2007), and even what separates “cool” people from “nerds” (“If you secretly like Michael Bolton, we’ll know,” Wired, October 2004). Reports on pathologies such as autism, in which neuroimaging plays a large role, are also common (for - stance, a Time magazine cover story from May 6, 2002, entitled “Inside the world of autism”).

Purely Functional Data Structures

Author : Chris Okasaki
Publisher : Cambridge University Press
ISBN 13 : 9780521663502
Total Pages : 236 pages
Book Rating : 4.6/5 (635 download)

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Book Synopsis Purely Functional Data Structures by : Chris Okasaki

Download or read book Purely Functional Data Structures written by Chris Okasaki and published by Cambridge University Press. This book was released on 1999-06-13 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes data structures and data structure design techniques for functional languages.

S+Functional Data Analysis

Author : Douglas B. Clarkson
Publisher : Springer Science & Business Media
ISBN 13 : 0387283935
Total Pages : 195 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis S+Functional Data Analysis by : Douglas B. Clarkson

Download or read book S+Functional Data Analysis written by Douglas B. Clarkson and published by Springer Science & Business Media. This book was released on 2006-06-02 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book can be considered a companion to two other highly acclaimed books involving James Ramsay and Bernard Silverman: Functional Data Analysis, Second Edition (2005) and Applied Functional Data Analysis (2002). This user's manual also provides the documentation for the S+FDA library for SPlus.