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Functional Data Analysis

Author: James Ramsay
Publisher: Springer Science & Business Media
ISBN: 147577107X
Size: 12.44 MB
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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.

Wahrscheinlichkeitstheorie Und Stochastische Prozesse

Author: Michael Mürmann
Publisher: Springer-Verlag
ISBN: 364238160X
Size: 26.43 MB
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Dieses Lehrbuch beschäftigt sich mit den zentralen Gebieten einer maßtheoretisch orientierten Wahrscheinlichkeitstheorie im Umfang einer zweisemestrigen Vorlesung. Nach den Grundlagen werden Grenzwertsätze und schwache Konvergenz behandelt. Es folgt die Darstellung und Betrachtung der stochastischen Abhängigkeit durch die bedingte Erwartung, die mit der Radon-Nikodym-Ableitung realisiert wird. Sie wird angewandt auf die Theorie der stochastischen Prozesse, die nach der allgemeinen Konstruktion aus der Untersuchung von Martingalen und Markov-Prozessen besteht. Neu in einem Lehrbuch über allgemeine Wahrscheinlichkeitstheorie ist eine Einführung in die stochastische Analysis von Semimartingalen auf der Grundlage einer geeigneten Stetigkeitsbedingung mit Anwendungen auf die Theorie der Finanzmärkte. Das Buch enthält zahlreiche Übungen, teilweise mit Lösungen. Neben der Theorie vertiefen Anmerkungen, besonders zu mathematischen Modellen für Phänomene der Realität, das Verständnis.​

Nonparametric Functional Data Analysis

Author: Frédéric Ferraty
Publisher: Springer Science & Business Media
ISBN: 0387366202
Size: 65.11 MB
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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.

Applied Functional Data Analysis

Author: J.O. Ramsay
Publisher: Springer
ISBN: 0387224653
Size: 59.74 MB
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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

Author: James Ramsay
Publisher: Springer Science & Business Media
ISBN: 0387981853
Size: 66.20 MB
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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 And Shape Data Analysis

Author: Anuj Srivastava
Publisher: Springer
ISBN: 1493940201
Size: 75.36 MB
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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.

Inference For Functional Data With Applications

Author: Lajos Horváth
Publisher: Springer Science & Business Media
ISBN: 1461436559
Size: 44.81 MB
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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.

Dynamic Data Analysis

Author: James Ramsay
Publisher: Springer
ISBN: 1493971905
Size: 57.22 MB
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This text focuses on the use of smoothing methods for developing and estimating differential equations following recent developments in functional data analysis and building on techniques described in Ramsay and Silverman (2005) Functional Data Analysis. The central concept of a dynamical system as a buffer that translates sudden changes in input into smooth controlled output responses has led to applications of previously analyzed data, opening up entirely new opportunities for dynamical systems. The technical level has been kept low so that those with little or no exposure to differential equations as modeling objects can be brought into this data analysis landscape. There are already many texts on the mathematical properties of ordinary differential equations, or dynamic models, and there is a large literature distributed over many fields on models for real world processes consisting of differential equations. However, a researcher interested in fitting such a model to data, or a statistician interested in the properties of differential equations estimated from data will find rather less to work with. This book fills that gap.

New Perspectives In Statistical Modeling And Data Analysis

Author: Salvatore Ingrassia
Publisher: Springer Science & Business Media
ISBN: 9783642113635
Size: 30.28 MB
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This volume provides recent research results in data analysis, classification and multivariate statistics and highlights perspectives for new scientific developments within these areas. Particular attention is devoted to methodological issues in clustering, statistical modeling and data mining. The volume also contains significant contributions to a wide range of applications such as finance, marketing, and social sciences. The papers in this volume were first presented at the 7th Conference of the Classification and Data Analysis Group (ClaDAG) of the Italian Statistical Society, held at the University of Catania, Italy.

S Functional Data Analysis

Author: Douglas B. Clarkson
Publisher: Springer Science & Business Media
ISBN: 0387283935
Size: 44.47 MB
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This book can be considered a companion to two other highly acclaimed books involving James Ramsay and Bernard Silverman: Functional Data Analysis, Second Edition (2005) and Applied Functional Data Analysis (2002). This user's manual also provides the documentation for the S+FDA library for S­Plus.