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Theoretical Foundations Of Functional Data Analysis With An Introduction To Linear Operators

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Theoretical Foundations Of Functional Data Analysis With An Introduction To Linear Operators

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Author : Tailen Hsing
language : en
Publisher: John Wiley & Sons
Release Date : 2015-04-07

Theoretical Foundations Of Functional Data Analysis With An Introduction To Linear Operators written by Tailen Hsing 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 2015-04-07 with Mathematics categories.

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.

Theoretical Foundations Of Functional Data Analysis With An Introduction To Linear Operators

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Author : Tailen Hsing
language : en
Publisher: John Wiley & Sons
Release Date : 2015-03-16

Introduction To Functional Data Analysis

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Author : Piotr Kokoszka
language : en
Publisher: CRC Press
Release Date : 2017-09-27

Introduction To Functional Data Analysis written by Piotr Kokoszka and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-27 with Mathematics categories.

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 Statistics And Related Fields

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Author : Germán Aneiros
language : en
Publisher: Springer
Release Date : 2017-04-25

Functional Statistics And Related Fields written by Germán Aneiros and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-25 with Mathematics categories.

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.

Cladag 2017 Book Of Short Papers

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Author : Francesca Greselin
language : en
Publisher: Universitas Studiorum
Release Date : 2017-09-29

Cladag 2017 Book Of Short Papers written by Francesca Greselin and has been published by Universitas Studiorum this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-29 with Mathematics categories.

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 High Dimensional Statistics And Related Fields

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Author : Germán Aneiros
language : en
Publisher: Springer Nature
Release Date : 2020-06-19

Functional And High Dimensional Statistics And Related Fields written by Germán Aneiros and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-19 with Mathematics categories.

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.

Novel Mathematics Inspired By Industrial Challenges

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Author : Michael Günther
language : en
Publisher: Springer Nature
Release Date : 2022-03-30

Novel Mathematics Inspired By Industrial Challenges written by Michael Günther and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-30 with Mathematics categories.

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.

International Encyclopedia Of Statistical Science

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Author : Miodrag Lovric
language : en
Publisher: Springer Nature
Release Date : 2025-06-19

International Encyclopedia Of Statistical Science written by Miodrag Lovric and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-19 with Mathematics categories.

The International Encyclopedia of Statistical Science stands as a monumental effort to enrich statistics education globally, particularly in regions facing educational challenges. By amalgamating the expertise of over 700 authors from 110 countries, including Nobel Laureates and presidents of statistical societies, it offers an unparalleled resource for readers worldwide. This encyclopedia is not just a collection of entries; it is a concerted effort to revive statistics as a vibrant, critical field of study and application. Providing a comprehensive and accessible account of statistical terms, methods, and applications, it enables readers to gain a quick insight into the subject, regardless of their background. This work serves to refresh and expand the knowledge of researchers, managers, and practitioners, highlighting the relevance and applicability of statistics across various fields, from economics and business to healthcare and public policy. Furthermore, it aims to inspire students by demonstrating the significance of statistics in solving real-world problems, thus encouraging a new generation to explore and contribute to the field.

Asymptotic Stochastics

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Author : Norbert Henze
language : en
Publisher: Springer Nature
Release Date : 2024-10-19

Asymptotic Stochastics written by Norbert Henze and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-19 with Mathematics categories.

This textbook, which is based on the second edition of a book that has been previously published in German language, provides a comprehension-oriented introduction to asymptotic stochastics. It is aimed at the beginning of a master's degree course in mathematics and covers the material that can be taught in a four-hour lecture with two-hour exercises. Individual chapters are also suitable for seminars at the end of a bachelor's degree course. In addition to more basic topics such as the method of moments in connection with the convergence in distribution or the multivariate central limit theorem and the delta method, the book covers limit theorems for U-statistics, the Wiener process and Donsker's theorem, as well as the Brownian bridge, with applications to statistics. It concludes with a central limit theorem for triangular arrays of Hilbert space-valued random elements with applications to weighted L2 statistics. The book is deliberately designed forself-study. It contains 138 self-questions, which are answered at the end of each chapter, as well as 194 exercises with solutions. This book is a translation of an original German edition. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.

New Trends In Functional Statistics And Related Fields

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Author : Germán Aneiros
language : en
Publisher: Springer Nature
Release Date : 2025-06-24

New Trends In Functional Statistics And Related Fields written by Germán Aneiros and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-24 with Mathematics categories.

This volume gathers peer-reviewed contributions presented at the 6th International Workshop on Functional and Operatorial Statistics, IWFOS 2025, held in Novara, Italy, June 25-27, 2025. Covering a broad spectrum of topics in functional and operatorial statistics and related fields, including high-dimensional statistics and machine learning, the contributions tackle both fundamental theoretical challenges and practical applications. A variety of features of statistics for functional data are addressed, such as estimation of functional features, exploration and pre-processing of functional data, methodologies for functional regression and forecasting problems, unsupervised and supervised classification, and testing procedures. Nonstandard functional data and situations which go beyond the pattern of samples of independent variables are investigated, and a link to the field of artificial intelligence is presented. Interesting real data applications to medicine, health, economics and the natural, environmental and social sciences are featured throughout. Initiated at the University of Toulouse in 2008, the series of IWFOS workshops fosters discussion and international collaboration on theoretical advancements, methodological innovations, and applications in functional and operatorial statistics and related fields. Chapter 42 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Theoretical Foundations Of Functional Data Analysis With An Introduction To Linear Operators

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