Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators van Tailen Hsing is a study book that clearly and systematically covers the theoretical foundations of functional data analysis (FDA). The book provides an in-depth description of the mathematical concepts and statistical methods that are essential for the analysis of functional data within Hilbert spaces.
Description
This publication provides a self-contained overview of functional analysis and operator theory, including reproducing kernel Hilbert spaces and singular value decompositions. The probabilistic underpinning from random elements in Hilbert spaces and continuous-time stochastic processes forms the basis of the FDA techniques discussed.
In addition, it introduces nonparametric estimation methods such as kernel smoothing and regularized smoothing for investigating the properties of estimators of, for example, mean elements, covariance operators, and principal components. It also presents a general approach to canonical correlations in Hilbert spaces, with which FDA models for factor analysis, regression, MANOVA, and discriminant analysis are developed.
The book is intended as a valuable reference work for researchers and statisticians who want to delve into the mathematical aspects of functional data analysis and complex statistical questions in this field.
Product specifications
- Author: Tailen Hsing (Professor, Department of Statistics, University of Michigan, USA)
- Series: Wiley Series in Probability and Statistics
- Publisher: John Wiley & Sons Inc
- Publication date: 2015-05-08
- Number of pages: 368
- ISBN: 9780470016916
- Topic: Functional analysis and transforms
- BISAC: MATHEMATICS / Functional Analysis
About the author
Tailen Hsing is a Professor at the University of Michigan and a Fellow of the International Statistical Institute and the Institute of Mathematical Statistics. His research includes, among other things, bioinformatics, extreme value theory, functional data analysis, and large-sample theory.
Randall Eubank is Professor Emeritus at Arizona State University and a respected expert in functional data analysis. He is known for his contributions to the field and for being a frequent invited speaker at international conferences.