Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators PDF full book. Access full book title Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators by Tailen Hsing. Download full books in PDF and EPUB format.
Author: Tailen Hsing
Publisher: John Wiley & Sons
ISBN: 0470016914
Category : Mathematics
Languages : en
Pages : 363
Get Book Here
Book Description
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.
Author: Tailen Hsing
Publisher: John Wiley & Sons
ISBN: 0470016914
Category : Mathematics
Languages : en
Pages : 363
Get Book Here
Book Description
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.
Author: Tailen Hsing
Publisher: John Wiley & Sons
ISBN: 1118762568
Category : Mathematics
Languages : en
Pages : 368
Get Book Here
Book Description
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.
Author: Piotr Kokoszka
Publisher: CRC Press
ISBN: 1498746691
Category : Mathematics
Languages : en
Pages : 371
Get Book Here
Book Description
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.
Author: Germán Aneiros
Publisher: Springer
ISBN: 3319558463
Category : Mathematics
Languages : en
Pages : 297
Get Book Here
Book Description
This volume collects latest methodological and applied contributions on functional, high-dimensional and other complex data, related statistical models and tools as well as on operator-based statistics. It contains selected and refereed contributions presented at the Fourth International Workshop on Functional and Operatorial Statistics (IWFOS 2017) held in A Coruña, Spain, from 15 to 17 June 2017. The series of IWFOS workshops was initiated by the Working Group on Functional and Operatorial Statistics at the University of Toulouse in 2008. Since then, many of the major advances in functional statistics and related fields have been periodically presented and discussed at the IWFOS workshops.
Author: Germán Aneiros
Publisher: Springer Nature
ISBN: 3030477568
Category : Mathematics
Languages : en
Pages : 254
Get Book Here
Book Description
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.
Author: Francesca Greselin
Publisher: Universitas Studiorum
ISBN: 8899459711
Category : Mathematics
Languages : en
Pages : 698
Get Book Here
Book Description
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.
Author: Michael Günther
Publisher: Springer Nature
ISBN: 3030961737
Category : Mathematics
Languages : en
Pages : 348
Get Book Here
Book Description
This contributed volume convenes a rich selection of works with a focus on innovative mathematical methods with applications in real-world, industrial problems. Studies included in this book are all motivated by a relevant industrial challenge, and demonstrate that mathematics for industry can be extremely rewarding, leading to new mathematical methods and sometimes even to entirely new fields within mathematics. The book is organized into two parts: Computational Sciences and Engineering, and Data Analysis and Finance. In every chapter, readers will find a brief description of why such work fits into this volume; an explanation on which industrial challenges have been instrumental for their inspiration; and which methods have been developed as a result. All these contribute to a greater unity of the text, benefiting not only practitioners and professionals seeking information on novel techniques but also graduate students in applied mathematics, engineering, and related fields.
Author: Stanisław Mazur
Publisher: Taylor & Francis
ISBN: 1000646122
Category : Business & Economics
Languages : en
Pages : 239
Get Book Here
Book Description
The radical transformations to which the economy and society have been subjected for decades have gained momentum in recent years, not least because of the coronavirus pandemic, the consequences of which are yet to be fully understood. As a result, certain economic models and business practices are becoming less sustainable. One of the reasons for this is the rapid advance of Revolution 4.0. The issues raised in this book are central to understanding the theoretical and practical aspects of the Fourth Industrial Revolution and its overwhelming impact on emerging socio-economic relations. The book addresses the future and flexibility of the labour market in the era of digital transformation; issues related to the emergence of new patterns of production and the distribution of public services. It examines the impact of Revolution 4.0 on the global business services sector and business project management models, in times of increasing complexity. The book covers a broad spectrum of concerns associated with Industry 4.0, such as social, economic, technological, and environmental, making it a comprehensive resource offering state-of-the-art knowledge. Further, it includes a discussion on the perspectives for the development of Revolution 4.0 in the context of the post-pandemic world. This book skillfully combines theoretical considerations with practical applications, offering a valuable, engaging and accessible resource for researchers, scholars, students, policymakers, public decision-makers, and businesspeople alike.
Author: Norbert Henze
Publisher: Springer Nature
ISBN: 3662689235
Category :
Languages : en
Pages : 470
Get Book Here
Book Description
Author: Ian L. Dryden
Publisher: John Wiley & Sons
ISBN: 0470699620
Category : Mathematics
Languages : en
Pages : 516
Get Book Here
Book Description
A thoroughly revised and updated edition of this introduction to modern statistical methods for shape analysis Shape analysis is an important tool in the many disciplines where objects are compared using geometrical features. Examples include comparing brain shape in schizophrenia; investigating protein molecules in bioinformatics; and describing growth of organisms in biology. This book is a significant update of the highly-regarded Statistical Shape Analysis by the same authors. The new edition lays the foundations of landmark shape analysis, including geometrical concepts and statistical techniques, and extends to include analysis of curves, surfaces, images and other types of object data. Key definitions and concepts are discussed throughout, and the relative merits of different approaches are presented. The authors have included substantial new material on recent statistical developments and offer numerous examples throughout the text. Concepts are introduced in an accessible manner, while retaining sufficient detail for more specialist statisticians to appreciate the challenges and opportunities of this new field. Computer code has been included for instructional use, along with exercises to enable readers to implement the applications themselves in R and to follow the key ideas by hands-on analysis. Offers a detailed yet accessible treatment of statistical methods for shape analysis Includes numerous examples and applications from many disciplines Provides R code for implementing the examples Covers a wide variety of recent developments in shape analysis Shape Analysis, with Applications in R will offer a valuable introduction to this fast-moving research area for statisticians and other applied scientists working in diverse areas, including archaeology, bioinformatics, biology, chemistry, computer science, medicine, morphometics and image analysis.
