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Bibliography Note: |
Includes bibliographical references (pages 327-330) and index. |
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Contents Note: |
Contents: Machine generated contents note: 1.Introduction -- 1.1.Multivariate analysis in a nutshell -- 1.2.The path that lies ahead -- 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 -- 3.Linear operator and functional -- 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.Frechet and Gateaux derivatives -- 3.7.Generalized Gram -- Schmidt decompositions -- 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 |
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Contents: Note continued: 8.3.Penalized least-squares estimation -- 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 -- 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 -- 11.Regression -- 11.1.A functional regression model -- 11.2.Asymptotic theory -- 11.3.Minimax optimality -- 11.4.Discretely sampled data. |
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Additional Physical Forms: |
Online version: Hsing, Tailen, 1955- Theoretical foundations of functional data analysis, with an introduction to linear operators. Chichester, West Sussex : John Wiley and Sons, Inc., 2015 ISBN 9781118762561 (DLC) 2015014859 |