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

• Main Authors: Hsing, Tailen (Author), Eubank, Randall L. 1952- (Author)
• Format: Book
• Language: English
• Published: Chichester, West Sussex, UK John Wiley 2015
• Series: Wiley series in probability and statistics
• Subjects: Multivariate analysis; Statistical functionals; Linear operators
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 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.