에너지경제연구원 전자도서관

로그인

에너지경제연구원 전자도서관

자료검색

  1. 메인
  2. 자료검색
  3. 통합검색

통합검색

단행본

Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Ope

발행사항
Chichester, West Sussex, UK : Wiley, 2015
형태사항
xiii, 333p. ; 24cm
서지주기
Includes bibliographical references (pages 327-330) and index
소장정보
위치등록번호청구기호 / 출력상태반납예정일
이용 가능 (1)
자료실E206948대출가능-
이용 가능 (1)
  • 등록번호
    E206948
    상태/반납예정일
    대출가능
    -
    위치/청구기호(출력)
    자료실
책 소개

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.



New feature

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 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.

Key features:

  • Provides a concise but rigorous account of the theoretical background of FDA
  • Introduces topics in various areas of mathematics, probability and statistics from the perspective of FDA
  • Presents a systematic exposition of the fundamental statistical issues in FDA
  • Develops all material from first principles, assuming no prior knowledge of linear operator or FDA

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.

목차
Preface 1 Introduction 2 Vector and function spaces 3 Linear operator and functionals 4 Compact operators and singular value decomposition 5 Perturbation theory 6 Smoothing and regularization 7 Random elements in a Hilbert space 8 Mean and covariance estimation 9 Principal components analysis 10 Canonical correlation analysis 11 Regression References Index Notation Index