Theoretical foundations of functional data analysis, with an introduction to linear operations / Tailsen Hsing, Randall Eubank.

Format:

Book

Author/Creator:

Hsing, Tailen., author.

Eubank, Randall, author.

Series:

Wiley series in probability and statistics.

Wiley Series in Probability and Statistics

Language:

English

Subjects (All):

Functional analysis.

Linear models (Statistics).

Stochastic processes.

Physical Description:

1 online resource (364 p.)

Edition:

1st edition

Place of Publication:

Chichester, England : Wiley, 2015.

Language Note:

English

System Details:

text file

Summary:

Provides essential coverage of functional data analysis and related areas.This book 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 perspecti

Contents:

Cover; Contents; Preface; Chapter 1 Introduction; 1.1 Multivariate analysis in a nutshell; 1.2 The path that lies ahead; Chapter 2 Vector and function spaces; 2.1 Metric spaces; 2.2 Vector and normed spaces; 2.3 Banach and Lp spaces; 2.4 Inner Product and Hilbert spaces; 2.5 The projection theorem and orthogonal decomposition; 2.6 Vector integrals; 2.7 Reproducing kernel Hilbert spaces; 2.8 Sobolev spaces; Chapter 3 Linear operator and functionals; 3.1 Operators; 3.2 Linear functionals; 3.3 Adjoint operator; 3.4 Nonnegative, square-root, and projection operators; 3.5 Operator inverses

3.6 Fréchet and Gâteaux derivatives3.7 Generalized Gram-Schmidt decompositions; Chapter 4 Compact operators and singular value decomposition; 4.1 Compact operators; 4.2 Eigenvalues of compact operators; 4.3 The singular value decomposition; 4.4 Hilbert-Schmidt operators; 4.5 Trace class operators; 4.6 Integral operators and Mercer's Theorem; 4.7 Operators on an RKHS; 4.8 Simultaneous diagonalization of two nonnegative definite operators; Chapter 5 Perturbation theory; 5.1 Perturbation of self-adjoint compact operators; 5.2 Perturbation of general compact operators

Chapter 6 Smoothing and regularization6.1 Functional linear model; 6.2 Penalized least squares estimators; 6.3 Bias and variance; 6.4 A computational formula; 6.5 Regularization parameter selection; 6.6 Splines; Chapter 7 Random elements in a Hilbert space; 7.1 Probability measures on a Hilbert space; 7.2 Mean and covariance of a random element of a Hilbert space; 7.3 Mean-square continuous processes and the Karhunen-Lòeve Theorem; 7.4 Mean-square continuous processes in L2(E, B(E),μ); 7.5 RKHS valued processes; 7.6 The closed span of a process; 7.7 Large sample theory

Chapter 8 Mean and covariance estimation8.1 Sample mean and covariance operator; 8.2 Local linear estimation; 8.3 Penalized least-squares estimation; Chapter 9 Principal components analysis; 9.1 Estimation via the sample covariance operator; 9.2 Estimation via local linear smoothing; 9.3 Estimation via penalized least squares; Chapter 10 Canonical correlation analysis; 10.1 CCA for random elements of a Hilbert space; 10.2 Estimation; 10.3 Prediction and regression; 10.4 Factor analysis; 10.5 MANOVA and discriminant analysis; 10.6 Orthogonal subspaces and partial cca; Chapter 11 Regression

11.1 A functional regression model11.2 Asymptotic theory; 11.3 Minimax optimality; 11.4 Discretely sampled data; References; Index; Notation Index; Wiley Series in Probability and Statistics; EULA

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (ebrary, viewed March 28, 2015).

ISBN:

9781118762578

1118762576

9781118762547

1118762541

9781118762561

1118762568

OCLC:

905348789