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Functional Data Analysis

2013-11-11 Mathematics
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Release : 2013-11-11
Genre : Mathematics
Kind : eBook
Book Rating : 07X/5 ( reviews)

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Book Synopsis Functional Data Analysis by : James Ramsay

Download or read book Functional Data Analysis written by James Ramsay. This book was released on 2013-11-11. 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

2017-09-27 Mathematics
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Release : 2017-09-27
Genre : Mathematics
Kind : eBook
Book Rating : 691/5 ( reviews)

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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. This book was released on 2017-09-27. 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.

Applied Functional Data Analysis

2007-11-23 Mathematics
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Release : 2007-11-23
Genre : Mathematics
Kind : eBook
Book Rating : 653/5 ( reviews)

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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. This book was released on 2007-11-23. 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.

Functional Data Analysis with R and MATLAB

2009-06-29 Computers
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Release : 2009-06-29
Genre : Computers
Kind : eBook
Book Rating : 853/5 ( reviews)

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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. This book was released on 2009-06-29. 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

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

2015-05-06 Mathematics
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Release : 2015-05-06
Genre : Mathematics
Kind : eBook
Book Rating : 914/5 ( reviews)

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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. This book was released on 2015-05-06. 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.

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