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

Author: Tailen Hsing
Publisher: John Wiley & Sons
ISBN: 1118762576
Size: 55.45 MB
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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.

Functional Statistics And Related Fields

Author: Germán Aneiros
Publisher: Springer
ISBN: 3319558463
Size: 23.12 MB
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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.

Moda 11 Advances In Model Oriented Design And Analysis

Author: Joachim Kunert
Publisher: Springer
ISBN: 3319312669
Size: 14.18 MB
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This volume contains pioneering contributions to both the theory and practice of optimal experimental design. Topics include the optimality of designs in linear and nonlinear models, as well as designs for correlated observations and for sequential experimentation. There is an emphasis on applications to medicine, in particular, to the design of clinical trials. Scientists from Europe, the US, Asia, Australia and Africa contributed to this volume of papers from the 11th Workshop on Model Oriented Design and Analysis.

Inference For Functional Data With Applications

Author: Lajos Horváth
Publisher: Springer Science & Business Media
ISBN: 1461436559
Size: 73.36 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.

Faltungsgleichungen Und Projektionsverfahren Zu Ihrer L Sung

Author: I. Gohberg
Publisher: Springer-Verlag
ISBN: 3034855117
Size: 26.87 MB
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VI A. S. MARKUS, A. A. SEMENCUL und 1. B. SIMONENKO für die Diskussionen über verschiedene Fragen und für ihre wertvollen Bemerkungen. Die Autoren bringen ihre Dankbarkeit dem Redakteur des Buches, F. V. SIROKOV, zum Ausdruck. Seine Hilfe trug maßgeblich zur einfachen und exakten Darlegung bei. Kisinev, am 18. Februar 1970 VORWORT ZUR DEUTSCHEN AUSGABE Die vorliegende Ausgabe dieses Buches unterscheidet sich nur in einem Teil wesentlich von dem russischen Original. Es handelt sich dabei um den Schluß des dritten Kapitels, wo Verfahren zur Umkehrung endlicher TOEPLITz-Matrizen und ihrer stetigen Analoga dargelegt werden. Die beiden letzten Paragraphen von KapitelIII (§ 6 und § 7) der russischen Ausgabe sind durch drei neue Paragraphen (§ 6, § 7, § 8) ersetzt worden. Die neue Darlegung ist vollständiger und zeichnet sich auch durch größere Allgemeinheit und Einfachheit aus. Darüber hinaus sind die Literaturhinweise sowie das Literaturverzeichnis er weitert worden. Es wurden einige unbedeutende Druckfehler berichtigt. Die Autoren danken aufrichtig Herrn Prof. Dr. S. PRÖSSDORF, der der Initiator dieser übersetzung ist, sowie dem Akademie-Verlag und den beiden übersetzern, Herrn Dr. J. LEITERER und Herrn Dr. R. LEHMANN. Kisinev Die Autoren 1. Mai 1972 INHALTSVERZEICHNIS Einführung ................................................................ 1 Kapitel I. Allgemeine Sätze über WIENER-HoPF-Gleichungen ...................... 9 § 1. Polynome von einseitig umkehrbaren Operatoren ......................... 9 1. Einige Hilfssätze. ................................................. 9 2. Einseitig umkehrbare Operatoren. . . . . . . . . . . . . . . . . . . . . . . . . . 11 . . . . . . . . . • 3. Umkehrung von Polynomen von einseitig umkehrbaren Operatoren. ...... 16 § 2. Stetige Funktionen von einseitig umkehrbaren Operatoren. . . . .. . . . . . . . . . 18 .

Representation Discovery Using Harmonic Analysis

Author: Sridhar Mahadevan
Publisher: Morgan & Claypool Publishers
ISBN: 1598296590
Size: 76.83 MB
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Representations are at the heart of artificial intelligence (AI). This book is devoted to the problem of representation discovery: how can an intelligent system construct representations from its experience? Representation discovery re-parameterizes the state space - prior to the application of information retrieval, machine learning, or optimization techniques - facilitating later inference processes by constructing new task-specific bases adapted to the state space geometry. This book presents a general approach to representation discovery using the framework of harmonic analysis, in particular Fourier and wavelet analysis. Biometric compression methods, the compact disc, the computerized axial tomography (CAT) scanner in medicine, JPEG compression, and spectral analysis of time-series data are among the many applications of classical Fourier and wavelet analysis. A central goal of this book is to show that these analytical tools can be generalized from their usual setting in (infinite-dimensional) Euclidean spaces to discrete (finite-dimensional) spaces typically studied in many subfields of AI. Generalizing harmonic analysis to discrete spaces poses many challenges: a discrete representation of the space must be adaptively acquired; basis functions are not pre-defined, but rather must be constructed. Algorithms for efficiently computing and representing bases require dealing with the curse of dimensionality. However, the benefits can outweigh the costs, since the extracted basis functions outperform parametric bases as they often reflect the irregular shape of a particular state space. Case studies from computer graphics, information retrieval, machine learning, and state space planning are used to illustrate the benefits of the proposed framework, and the challenges that remain to be addressed. Representation discovery is an actively developing field, and the author hopes this book will encourage other researchers to explore this exciting area of research.

Einf Hrung In Die Funktionalanalysis

Author: Reinhold Meise
Publisher: Springer-Verlag
ISBN: 3322803104
Size: 20.56 MB
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Dieses Buch wendet sich an Studenten der Mathematik und der Physik, welche über Grundkenntnisse in Analysis und linearer Algebra verfügen.

Partielle Differentialgleichungen Der Geometrie Und Der Physik 2

Author: Friedrich Sauvigny
Publisher: Springer-Verlag
ISBN: 3540275401
Size: 11.75 MB
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Das zweibändige Lehrbuch behandelt das Gebiet der partiellen Differentialgleichungen umfassend und anschaulich. Der Autor stellt in Band 2 funktionalanalytische Lösungsmethoden vor und erläutert u. a. die Lösbarkeit von Operatorgleichungen im Banachraum, lineare Operatoren im Hilbertraum und Spektraltheorie, die Schaudersche Theorie linearer elliptischer Differentialgleichungen sowie schwache Lösungen elliptischer Differentialgleichungen.

Understanding Robust And Exploratory Data Analysis

Author: David Caster Hoaglin
Publisher: Wiley-Interscience
ISBN:
Size: 23.86 MB
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The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensiveeditions, Wiley hopes to extend the life of these important works by making themavailable to future generations of mathematicians and scientists. Currently available in the Series: T.W. Anderson The Statistical Analysis of Time Series T.S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic Processes with Applications to the Natural Sciences Robert G. Bartle The Elements of Integration and Lebesgue Measure George E. P. Box & Norman R. Draper Evolutionary Operation: A Statistical Method for Process Improvement George E. P. Box & George C. Tiao Bayesian Inference in Statistical Analysis R. W. Carter Finite Groups of Lie Type: Conjugacy Classes and Complex Characters R. W. Carter Simple Groups of Lie Type William G. Cochran & Gertrude M. Cox Experimental Designs, Second Edition Richard Courant Differential and Integral Calculus, Volume I Richard Courant Differential and Integral Calculus, Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume II D. R. Cox Planning of Experiments Harold S. M. Coxeter Introduction to Geometry, Second Edition Charles W. Curtis & Irving Reiner Representation Theory of Finite Groups and Associative Algebras Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume I Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume II Cuthbert Daniel Fitting Equations to Data: Computer Analysis of Multifactor Data, Second Edition Bruno de Finetti Theory of Probability, Volume I Bruno de Finetti Theory of Probability, Volume 2 W. Edwards Deming Sample Design in Business Research Amos de Shalit & Herman Feshbach Theoretical Nuclear Physics, Volume 1— Nuclear Structure Harold F. Dodge & Harry G. Romig Sampling Inspection Tables: Single and Double Sampling J. L. Doob Stochastic Processes Nelson Dunford & Jacob T. Schwartz Linear Operators, Part One, General Theory Nelson Dunford & Jacob T. Schwartz Linear Operators, Part Two, Spectral Theory—Self Adjoint Operators in Hilbert Space Nelson Dunford & Jacob T. Schwartz Linear Operators, Part Three, Spectral Operators Regina C. Elandt-Johnson & Norman L. Johnson Survival Models and Data Analysis Herman Feshbach Theoretical Nuclear Physics: Nuclear Reactions Joseph L. Fleiss Design and Analysis of Clinical Experiments Bernard Friedman Lectures on Applications-Oriented Mathematics Phillip Griffiths & Joseph Harris Principles of Algebraic Geometry Gerald J. Hahn & Samuel S. Shapiro Statistical Models in Engineering Marshall Hall, Jr. Combinatorial Theory, Second Edition Morris H. Hansen, William N. Hurwitz & William G. Madow Sample Survey Methods and Theory, Volume I—Methods and Applications Morris H. Hansen, William N. Hurwitz & William G. Madow Sample Survey Methods and Theory, Volume II—Theory Peter Henrici Applied and Computational Complex Analysis, Volume 1—Power Series—Integration—Conformal Mapping—Location of Zeros Peter Henrici Applied and Computational Complex Analysis, Volume 2—Special Functions—Integral Transforms—Asymptotics—Continued Fractions Peter Henrici Applied and Computational Complex Analysis, Volume 3—Discrete Fourier Analysis—Cauchy Integrals—Construction of Conformal Maps—Univalent Functions Peter Hilton & Yel-Chiang Wu A Course in Modern Algebra David C. Hoaglin, Frederick Mosteller & John W. Tukey Understanding Robust and Exploratory Data Analysis Harry Hochstadt Integral Equations Leslie Kish Survey Sampling Shoshichi Kobayashi & Katsumi Nomizu Foundations of Differential Geometry, Volume I Shoshichi Kobayashi & Katsumi Nomizu Foundations of Differential Geometry, Volume 2 Erwin O. Kreyszig Introductory Functional Analysis with Applications William H. Louisell Quantum Statistical Properties of Radiation Rupert G. Miller Jr. Survival Analysis Ali Hasan Nayfeh Introduction to Perturbation Techniques Ali Hasan Nayfeh & Dean T. Mook Nonlinear Oscillations Emanuel Parzen Modern Probability Theory & Its Applications P. M. Prenter Splines and Variational Methods Howard Raiffa & Robert Schlaifer Applied Statistical Decision Theory Walter Rudin Fourier Analysis on Groups Lawrence S. Schulman Techniques and Applications of Path Integration Shayle R. Searle Linear Models I. H. Segel Enzyme Kinetics: Behavior and Analysis of Rapid Equilibrium and Steady-State Enzyme Systems C. L. Siegel Topics in Complex Function Theory, Volume I—Elliptic Functions and Uniformization Theory C. L. Siegel Topics in Complex Function Theory, Volume II—Automorphic and Abelian Integrals C. L. Siegel Topics in Complex Function Theory, Volume III—Abelian Functions and Modular Functions of Several Variables L. Spitzer Physical Processes in the Interstellar Medium J. J. Stoker Differential Geometry J. J. Stoker Water Waves: The Mathematical Theory with Applications J. J. Stoker Nonlinear Vibrations in Mechanical and ElectricalSystems Richard Zallen The Physics of Amorphous Solids Arnold Zellner Introduction to Bayesian Inference in Econometrics

Geometry Morphology And Computational Imaging

Author: Tetsuo Asano
Publisher: Springer Science & Business Media
ISBN: 3540009167
Size: 16.76 MB
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This book constitutes the thoroughly refereed post-proceedings of the 11th International Workshop on Theoretical Foundations of Computer Vision, held in Dagstuhl Castle, Germany in April 2002. The 27 revised full papers presented went through two rounds of reviewing and improvement and assess the state of the art in geometry, morphology, and computational imaging. The papers are organized in sections on geometry - models and algorithms; property measurement in the grid and on finite samples; features, shape, and morphology; and computer vision and scene analysis.