Inference For Functional Data With Applications

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Inference for Functional Data with Applications

Lajos Horváth,Piotr Kokoszka
Inference for Functional Data with Applications Book PDF

Author : Lajos Horváth,Piotr Kokoszka
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 51,9 Mb
Release : 2012-05-08
Category : Mathematics
ISBN : 9781461436553

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Inference for Functional Data with Applications by Lajos Horváth,Piotr Kokoszka Pdf

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.

Functional Data Analysis with R and MATLAB

James Ramsay,Giles Hooker,Spencer Graves
Functional Data Analysis with R and MATLAB Book PDF

Author : James Ramsay,Giles Hooker,Spencer Graves
Publisher : Springer Science & Business Media
Page : 213 pages
File Size : 53,8 Mb
Release : 2009-06-29
Category : Computers
ISBN : 9780387981857

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Functional Data Analysis with R and MATLAB by James Ramsay,Giles Hooker,Spencer Graves Pdf

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 Data Analysis with R

Ciprian M. Crainiceanu,Jeff Goldsmith,Andrew Leroux,Erjia Cui
Functional Data Analysis with R Book PDF

Author : Ciprian M. Crainiceanu,Jeff Goldsmith,Andrew Leroux,Erjia Cui
Publisher : CRC Press
Page : 338 pages
File Size : 55,5 Mb
Release : 2024-03-11
Category : Mathematics
ISBN : 9781003856306

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Functional Data Analysis with R by Ciprian M. Crainiceanu,Jeff Goldsmith,Andrew Leroux,Erjia Cui Pdf

Emerging technologies generate data sets of increased size and complexity that require new or updated statistical inferential methods and scalable, reproducible software. These data sets often involve measurements of a continuous underlying process, and benefit from a functional data perspective. Functional Data Analysis with R presents many ideas for handling functional data including dimension reduction techniques, smoothing, functional regression, structured decompositions of curves, and clustering. The idea is for the reader to be able to immediately reproduce the results in the book, implement these methods, and potentially design new methods and software that may be inspired by these approaches. Features: Functional regression models receive a modern treatment that allows extensions to many practical scenarios and development of state-of-the-art software. The connection between functional regression, penalized smoothing, and mixed effects models is used as the cornerstone for inference. Multilevel, longitudinal, and structured functional data are discussed with emphasis on emerging functional data structures. Methods for clustering functional data before and after smoothing are discussed. Multiple new functional data sets with dense and sparse sampling designs from various application areas are presented, including the NHANES linked accelerometry and mortality data, COVID-19 mortality data, CD4 counts data, and the CONTENT child growth study. Step-by-step software implementations are included, along with a supplementary website (www.FunctionalDataAnalysis.com) featuring software, data, and tutorials. More than 100 plots for visualization of functional data are presented. Functional Data Analysis with R is primarily aimed at undergraduate, master's, and PhD students, as well as data scientists and researchers working on functional data analysis. The book can be read at different levels and combines state-of-the-art software, methods, and inference. It can be used for self-learning, teaching, and research, and will particularly appeal to anyone who is interested in practical methods for hands-on, problem-forward functional data analysis. The reader should have some basic coding experience, but expertise in R is not required.

Geostatistical Functional Data Analysis

Jorge Mateu,Ramon Giraldo
Geostatistical Functional Data Analysis Book PDF

Author : Jorge Mateu,Ramon Giraldo
Publisher : John Wiley & Sons
Page : 452 pages
File Size : 48,6 Mb
Release : 2021-12-13
Category : Social Science
ISBN : 9781119387848

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Geostatistical Functional Data Analysis by Jorge Mateu,Ramon Giraldo Pdf

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.

Introduction to Functional Data Analysis

Piotr Kokoszka,Matthew Reimherr
Introduction to Functional Data Analysis Book PDF

Author : Piotr Kokoszka,Matthew Reimherr
Publisher : CRC Press
Page : 311 pages
File Size : 44,6 Mb
Release : 2017-09-27
Category : Mathematics
ISBN : 9781498746694

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Introduction to Functional Data Analysis by Piotr Kokoszka,Matthew Reimherr Pdf

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.

Introduction to Functional Data Analysis

Piotr Kokoszka,Matthew Reimherr
Introduction to Functional Data Analysis Book PDF

Author : Piotr Kokoszka,Matthew Reimherr
Publisher : CRC Press
Page : 307 pages
File Size : 44,5 Mb
Release : 2017-09-27
Category : Mathematics
ISBN : 9781498746625

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Introduction to Functional Data Analysis by Piotr Kokoszka,Matthew Reimherr Pdf

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.

Analysis of Variance for Functional Data

Jin-Ting Zhang
Analysis of Variance for Functional Data Book PDF

Author : Jin-Ting Zhang
Publisher : CRC Press
Page : 412 pages
File Size : 46,5 Mb
Release : 2013-06-18
Category : Mathematics
ISBN : 9781439862742

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Analysis of Variance for Functional Data by Jin-Ting Zhang Pdf

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.

Recent Advances in Functional Data Analysis and Related Topics

Frédéric Ferraty
Recent Advances in Functional Data Analysis and Related Topics Book PDF

Author : Frédéric Ferraty
Publisher : Springer Science & Business Media
Page : 322 pages
File Size : 49,5 Mb
Release : 2011-06-15
Category : Mathematics
ISBN : 9783790827361

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Recent Advances in Functional Data Analysis and Related Topics by Frédéric Ferraty Pdf

New technologies allow us to handle increasingly large datasets, while monitoring devices are becoming ever more sophisticated. This high-tech progress produces statistical units sampled over finer and finer grids. As the measurement points become closer, the data can be considered as observations varying over a continuum. This intrinsic continuous data (called functional data) can be found in various fields of science, including biomechanics, chemometrics, econometrics, environmetrics, geophysics, medicine, etc. The failure of standard multivariate statistics to analyze such functional data has led the statistical community to develop appropriate statistical methodologies, called Functional Data Analysis (FDA). Today, FDA is certainly one of the most motivating and popular statistical topics due to its impact on crucial societal issues (health, environment, etc). This is why the FDA statistical community is rapidly growing, as are the statistical developments . Therefore, it is necessary to organize regular meetings in order to provide a state-of-art review of the recent advances in this fascinating area. This book collects selected and extended papers presented at the second International Workshop of Functional and Operatorial Statistics (Santander, Spain, 16-18 June, 2011), in which many outstanding experts on FDA will present the most relevant advances in this pioneering statistical area. Undoubtedly, these proceedings will be an essential resource for academic researchers, master students, engineers, and practitioners not only in statistics but also in numerous related fields of application.

Wavelets in Functional Data Analysis

Pedro A. Morettin,Aluísio Pinheiro,Brani Vidakovic
Wavelets in Functional Data Analysis Book PDF

Author : Pedro A. Morettin,Aluísio Pinheiro,Brani Vidakovic
Publisher : Springer
Page : 106 pages
File Size : 55,7 Mb
Release : 2017-11-07
Category : Mathematics
ISBN : 9783319596235

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Wavelets in Functional Data Analysis by Pedro A. Morettin,Aluísio Pinheiro,Brani Vidakovic Pdf

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.

Functional Data Analysis

James Ramsay,B. W. Silverman
Functional Data Analysis Book PDF

Author : James Ramsay,B. W. Silverman
Publisher : Springer Science & Business Media
Page : 317 pages
File Size : 48,6 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475771077

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Functional Data Analysis by James Ramsay,B. W. Silverman Pdf

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.

Functional and High-Dimensional Statistics and Related Fields

Germán Aneiros,Ivana Horová,Marie Hušková,Philippe Vieu
Functional and High Dimensional Statistics and Related Fields Book PDF

Author : Germán Aneiros,Ivana Horová,Marie Hušková,Philippe Vieu
Publisher : Springer Nature
Page : 254 pages
File Size : 41,6 Mb
Release : 2020-06-19
Category : Mathematics
ISBN : 9783030477561

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Functional and High-Dimensional Statistics and Related Fields by Germán Aneiros,Ivana Horová,Marie Hušková,Philippe Vieu Pdf

This book presents the latest research on the statistical analysis of functional, high-dimensional and other complex data, addressing methodological and computational aspects, as well as real-world applications. It covers topics like classification, confidence bands, density estimation, depth, diagnostic tests, dimension reduction, estimation on manifolds, high- and infinite-dimensional statistics, inference on functional data, networks, operatorial statistics, prediction, regression, robustness, sequential learning, small-ball probability, smoothing, spatial data, testing, and topological object data analysis, and includes applications in automobile engineering, criminology, drawing recognition, economics, environmetrics, medicine, mobile phone data, spectrometrics and urban environments. The book gathers selected, refereed contributions presented at the Fifth International Workshop on Functional and Operatorial Statistics (IWFOS) in Brno, Czech Republic. The workshop was originally to be held on June 24-26, 2020, but had to be postponed as a consequence of the COVID-19 pandemic. Initiated by the Working Group on Functional and Operatorial Statistics at the University of Toulouse in 2008, the IWFOS workshops provide a forum to discuss the latest trends and advances in functional statistics and related fields, and foster the exchange of ideas and international collaboration in the field.

Cladag 2017 Book of Short Papers

Francesca Greselin,Francesco Mola,Mariangela Zenga
Cladag 2017 Book of Short Papers Book PDF

Author : Francesca Greselin,Francesco Mola,Mariangela Zenga
Publisher : Universitas Studiorum
Page : 698 pages
File Size : 54,8 Mb
Release : 2017-09-29
Category : Mathematics
ISBN : 9788899459710

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Cladag 2017 Book of Short Papers by Francesca Greselin,Francesco Mola,Mariangela Zenga Pdf

This book is the collection of the Abstract / Short Papers submitted by the authors of the International Conference of The CLAssification and Data Analysis Group (CLADAG) of the Italian Statistical Society (SIS), held in Milan (Italy) on September 13-15, 2017.

Functional and Shape Data Analysis

Anuj Srivastava,Eric P. Klassen
Functional and Shape Data Analysis Book PDF

Author : Anuj Srivastava,Eric P. Klassen
Publisher : Springer
Page : 447 pages
File Size : 40,5 Mb
Release : 2016-10-03
Category : Mathematics
ISBN : 9781493940202

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Functional and Shape Data Analysis by Anuj Srivastava,Eric P. Klassen Pdf

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.

Functional and High-Dimensional Statistics and Related Fields

Germán Aneiros,Ivana Horová,Marie Hušková,Philippe Vieu
Functional and High Dimensional Statistics and Related Fields Book PDF

Author : Germán Aneiros,Ivana Horová,Marie Hušková,Philippe Vieu
Publisher : Springer
Page : 254 pages
File Size : 41,7 Mb
Release : 2021-06-21
Category : Mathematics
ISBN : 3030477584

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Functional and High-Dimensional Statistics and Related Fields by Germán Aneiros,Ivana Horová,Marie Hušková,Philippe Vieu Pdf

This book presents the latest research on the statistical analysis of functional, high-dimensional and other complex data, addressing methodological and computational aspects, as well as real-world applications. It covers topics like classification, confidence bands, density estimation, depth, diagnostic tests, dimension reduction, estimation on manifolds, high- and infinite-dimensional statistics, inference on functional data, networks, operatorial statistics, prediction, regression, robustness, sequential learning, small-ball probability, smoothing, spatial data, testing, and topological object data analysis, and includes applications in automobile engineering, criminology, drawing recognition, economics, environmetrics, medicine, mobile phone data, spectrometrics and urban environments. The book gathers selected, refereed contributions presented at the Fifth International Workshop on Functional and Operatorial Statistics (IWFOS) in Brno, Czech Republic. The workshop was originally to be held on June 24-26, 2020, but had to be postponed as a consequence of the COVID-19 pandemic. Initiated by the Working Group on Functional and Operatorial Statistics at the University of Toulouse in 2008, the IWFOS workshops provide a forum to discuss the latest trends and advances in functional statistics and related fields, and foster the exchange of ideas and international collaboration in the field.

Functional Data Analysis

James Ramsay,B. W. Silverman
Functional Data Analysis Book PDF

Author : James Ramsay,B. W. Silverman
Publisher : Springer Science & Business Media
Page : 464 pages
File Size : 48,5 Mb
Release : 2005-06-08
Category : Mathematics
ISBN : 038740080X

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Functional Data Analysis by James Ramsay,B. W. Silverman Pdf

This is the second edition of a highly succesful book which has sold nearly 3000 copies world wide since its publication in 1997. Many chapters will be rewritten and expanded due to a lot of progress in these areas since the publication of the first edition. Bernard Silverman is the author of two other books, each of which has lifetime sales of more than 4000 copies. He has a great reputation both as a researcher and an author. This is likely to be the bestselling book in the Springer Series in Statistics for a couple of years.