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

✅ 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.

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