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Principal Component Models For Sparse Functional Data
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Book Synopsis Linear Processes in Function Spaces by : Denis Bosq
Download or read book Linear Processes in Function Spaces written by Denis Bosq and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main subject of this book is the estimation and forecasting of continuous time processes. It leads to a development of the theory of linear processes in function spaces. Mathematical tools are presented, as well as autoregressive processes in Hilbert and Banach spaces and general linear processes and statistical prediction. Implementation and numerical applications are also covered. The book assumes knowledge of classical probability theory and statistics.
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
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 371 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.
Book Synopsis Generalized Principal Component Analysis by : René Vidal
Download or read book Generalized Principal Component Analysis written by René Vidal and published by Springer. This book was released on 2016-04-11 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to the latest advances in the mathematical theory and computational tools for modeling high-dimensional data drawn from one or multiple low-dimensional subspaces (or manifolds) and potentially corrupted by noise, gross errors, or outliers. This challenging task requires the development of new algebraic, geometric, statistical, and computational methods for efficient and robust estimation and segmentation of one or multiple subspaces. The book also presents interesting real-world applications of these new methods in image processing, image and video segmentation, face recognition and clustering, and hybrid system identification etc. This book is intended to serve as a textbook for graduate students and beginning researchers in data science, machine learning, computer vision, image and signal processing, and systems theory. It contains ample illustrations, examples, and exercises and is made largely self-contained with three Appendices which survey basic concepts and principles from statistics, optimization, and algebraic-geometry used in this book. René Vidal is a Professor of Biomedical Engineering and Director of the Vision Dynamics and Learning Lab at The Johns Hopkins University. Yi Ma is Executive Dean and Professor at the School of Information Science and Technology at ShanghaiTech University. S. Shankar Sastry is Dean of the College of Engineering, Professor of Electrical Engineering and Computer Science and Professor of Bioengineering at the University of California, Berkeley.
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.
Book Synopsis Recent Advances in Functional Data Analysis and Related Topics by : Frédéric Ferraty
Download or read book Recent Advances in Functional Data Analysis and Related Topics written by Frédéric Ferraty and published by Springer Science & Business Media. This book was released on 2011-06-15 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Book Synopsis Richly Parameterized Linear Models by : James S. Hodges
Download or read book Richly Parameterized Linear Models written by James S. Hodges and published by CRC Press. This book was released on 2016-04-19 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: A First Step toward a Unified Theory of Richly Parameterized Linear ModelsUsing mixed linear models to analyze data often leads to results that are mysterious, inconvenient, or wrong. Further compounding the problem, statisticians lack a cohesive resource to acquire a systematic, theory-based understanding of models with random effects.Richly Param
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 406 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 l
Book Synopsis Statistics for Spatio-Temporal Data by : Noel Cressie
Download or read book Statistics for Spatio-Temporal Data written by Noel Cressie and published by John Wiley & Sons. This book was released on 2015-11-02 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: Winner of the 2013 DeGroot Prize. A state-of-the-art presentation of spatio-temporal processes, bridging classic ideas with modern hierarchical statistical modeling concepts and the latest computational methods Noel Cressie and Christopher K. Wikle, are also winners of the 2011 PROSE Award in the Mathematics category, for the book “Statistics for Spatio-Temporal Data” (2011), published by John Wiley and Sons. (The PROSE awards, for Professional and Scholarly Excellence, are given by the Association of American Publishers, the national trade association of the US book publishing industry.) Statistics for Spatio-Temporal Data has now been reprinted with small corrections to the text and the bibliography. The overall content and pagination of the new printing remains the same; the difference comes in the form of corrections to typographical errors, editing of incomplete and missing references, and some updated spatio-temporal interpretations. From understanding environmental processes and climate trends to developing new technologies for mapping public-health data and the spread of invasive-species, there is a high demand for statistical analyses of data that take spatial, temporal, and spatio-temporal information into account. Statistics for Spatio-Temporal Data presents a systematic approach to key quantitative techniques that incorporate the latest advances in statistical computing as well as hierarchical, particularly Bayesian, statistical modeling, with an emphasis on dynamical spatio-temporal models. Cressie and Wikle supply a unique presentation that incorporates ideas from the areas of time series and spatial statistics as well as stochastic processes. Beginning with separate treatments of temporal data and spatial data, the book combines these concepts to discuss spatio-temporal statistical methods for understanding complex processes. Topics of coverage include: Exploratory methods for spatio-temporal data, including visualization, spectral analysis, empirical orthogonal function analysis, and LISAs Spatio-temporal covariance functions, spatio-temporal kriging, and time series of spatial processes Development of hierarchical dynamical spatio-temporal models (DSTMs), with discussion of linear and nonlinear DSTMs and computational algorithms for their implementation Quantifying and exploring spatio-temporal variability in scientific applications, including case studies based on real-world environmental data Throughout the book, interesting applications demonstrate the relevance of the presented concepts. Vivid, full-color graphics emphasize the visual nature of the topic, and a related FTP site contains supplementary material. Statistics for Spatio-Temporal Data is an excellent book for a graduate-level course on spatio-temporal statistics. It is also a valuable reference for researchers and practitioners in the fields of applied mathematics, engineering, and the environmental and health sciences.
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.
Book Synopsis Mixed Effects Models for Complex Data by : Lang Wu
Download or read book Mixed Effects Models for Complex Data written by Lang Wu and published by CRC Press. This book was released on 2009-11-11 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although standard mixed effects models are useful in a range of studies, other approaches must often be used in correlation with them when studying complex or incomplete data. Mixed Effects Models for Complex Data discusses commonly used mixed effects models and presents appropriate approaches to address dropouts, missing data, measurement errors, censoring, and outliers. For each class of mixed effects model, the author reviews the corresponding class of regression model for cross-sectional data. An overview of general models and methods, along with motivating examples After presenting real data examples and outlining general approaches to the analysis of longitudinal/clustered data and incomplete data, the book introduces linear mixed effects (LME) models, generalized linear mixed models (GLMMs), nonlinear mixed effects (NLME) models, and semiparametric and nonparametric mixed effects models. It also includes general approaches for the analysis of complex data with missing values, measurement errors, censoring, and outliers. Self-contained coverage of specific topics Subsequent chapters delve more deeply into missing data problems, covariate measurement errors, and censored responses in mixed effects models. Focusing on incomplete data, the book also covers survival and frailty models, joint models of survival and longitudinal data, robust methods for mixed effects models, marginal generalized estimating equation (GEE) models for longitudinal or clustered data, and Bayesian methods for mixed effects models. Background material In the appendix, the author provides background information, such as likelihood theory, the Gibbs sampler, rejection and importance sampling methods, numerical integration methods, optimization methods, bootstrap, and matrix algebra. Failure to properly address missing data, measurement errors, and other issues in statistical analyses can lead to severely biased or misleading results. This book explores the biases that arise when naïve methods are used and shows which approaches should be used to achieve accurate results in longitudinal data analysis.
Book Synopsis Statistical Parametric Mapping: The Analysis of Functional Brain Images by : William D. Penny
Download or read book Statistical Parametric Mapping: The Analysis of Functional Brain Images written by William D. Penny and published by Elsevier. This book was released on 2011-04-28 with total page 689 pages. Available in PDF, EPUB and Kindle. Book excerpt: In an age where the amount of data collected from brain imaging is increasing constantly, it is of critical importance to analyse those data within an accepted framework to ensure proper integration and comparison of the information collected. This book describes the ideas and procedures that underlie the analysis of signals produced by the brain. The aim is to understand how the brain works, in terms of its functional architecture and dynamics. This book provides the background and methodology for the analysis of all types of brain imaging data, from functional magnetic resonance imaging to magnetoencephalography. Critically, Statistical Parametric Mapping provides a widely accepted conceptual framework which allows treatment of all these different modalities. This rests on an understanding of the brain's functional anatomy and the way that measured signals are caused experimentally. The book takes the reader from the basic concepts underlying the analysis of neuroimaging data to cutting edge approaches that would be difficult to find in any other source. Critically, the material is presented in an incremental way so that the reader can understand the precedents for each new development. This book will be particularly useful to neuroscientists engaged in any form of brain mapping; who have to contend with the real-world problems of data analysis and understanding the techniques they are using. It is primarily a scientific treatment and a didactic introduction to the analysis of brain imaging data. It can be used as both a textbook for students and scientists starting to use the techniques, as well as a reference for practicing neuroscientists. The book also serves as a companion to the software packages that have been developed for brain imaging data analysis. - An essential reference and companion for users of the SPM software - Provides a complete description of the concepts and procedures entailed by the analysis of brain images - Offers full didactic treatment of the basic mathematics behind the analysis of brain imaging data - Stands as a compendium of all the advances in neuroimaging data analysis over the past decade - Adopts an easy to understand and incremental approach that takes the reader from basic statistics to state of the art approaches such as Variational Bayes - Structured treatment of data analysis issues that links different modalities and models - Includes a series of appendices and tutorial-style chapters that makes even the most sophisticated approaches accessible
Book Synopsis Complex Data Modeling and Computationally Intensive Statistical Methods by : Pietro Mantovan
Download or read book Complex Data Modeling and Computationally Intensive Statistical Methods written by Pietro Mantovan and published by Springer Science & Business Media. This book was released on 2011-01-27 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: Selected from the conference "S.Co.2009: Complex Data Modeling and Computationally Intensive Methods for Estimation and Prediction," these 20 papers cover the latest in statistical methods and computational techniques for complex and high dimensional datasets.
Book Synopsis Object Oriented Data Analysis by : J. S. Marron
Download or read book Object Oriented Data Analysis written by J. S. Marron and published by CRC Press. This book was released on 2021-11-18 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Object Oriented Data Analysis is a framework that facilitates inter-disciplinary research through new terminology for discussing the often many possible approaches to the analysis of complex data. Such data are naturally arising in a wide variety of areas. This book aims to provide ways of thinking that enable the making of sensible choices. The main points are illustrated with many real data examples, based on the authors' personal experiences, which have motivated the invention of a wide array of analytic methods. While the mathematics go far beyond the usual in statistics (including differential geometry and even topology), the book is aimed at accessibility by graduate students. There is deliberate focus on ideas over mathematical formulas. J. S. Marron is the Amos Hawley Distinguished Professor of Statistics, Professor of Biostatistics, Adjunct Professor of Computer Science, Faculty Member of the Bioinformatics and Computational Biology Curriculum and Research Member of the Lineberger Cancer Center and the Computational Medicine Program, at the University of North Carolina, Chapel Hill. Ian L. Dryden is a Professor in the Department of Mathematics and Statistics at Florida International University in Miami, has served as Head of School of Mathematical Sciences at the University of Nottingham, and is joint author of the acclaimed book Statistical Shape Analysis.
Book Synopsis Nonparametric Models for Longitudinal Data by : Colin O. Wu
Download or read book Nonparametric Models for Longitudinal Data written by Colin O. Wu and published by CRC Press. This book was released on 2018-05-23 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonparametric Models for Longitudinal Data with Implementations in R presents a comprehensive summary of major advances in nonparametric models and smoothing methods with longitudinal data. It covers methods, theories, and applications that are particularly useful for biomedical studies in the era of big data and precision medicine. It also provides flexible tools to describe the temporal trends, covariate effects and correlation structures of repeated measurements in longitudinal data. This book is intended for graduate students in statistics, data scientists and statisticians in biomedical sciences and public health. As experts in this area, the authors present extensive materials that are balanced between theoretical and practical topics. The statistical applications in real-life examples lead into meaningful interpretations and inferences. Features: • Provides an overview of parametric and semiparametric methods • Shows smoothing methods for unstructured nonparametric models • Covers structured nonparametric models with time-varying coefficients • Discusses nonparametric shared-parameter and mixed-effects models • Presents nonparametric models for conditional distributions and functionals • Illustrates implementations using R software packages • Includes datasets and code in the authors’ website • Contains asymptotic results and theoretical derivations
Book Synopsis Independent Component Analysis by : Aapo Hyvärinen
Download or read book Independent Component Analysis written by Aapo Hyvärinen and published by John Wiley & Sons. This book was released on 2004-04-05 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to ICA for students and practitioners Independent Component Analysis (ICA) is one of the most exciting new topics in fields such as neural networks, advanced statistics, and signal processing. This is the first book to provide a comprehensive introduction to this new technique complete with the fundamental mathematical background needed to understand and utilize it. It offers a general overview of the basics of ICA, important solutions and algorithms, and in-depth coverage of new applications in image processing, telecommunications, audio signal processing, and more. Independent Component Analysis is divided into four sections that cover: * General mathematical concepts utilized in the book * The basic ICA model and its solution * Various extensions of the basic ICA model * Real-world applications for ICA models Authors Hyvarinen, Karhunen, and Oja are well known for their contributions to the development of ICA and here cover all the relevant theory, new algorithms, and applications in various fields. Researchers, students, and practitioners from a variety of disciplines will find this accessible volume both helpful and informative.
