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Wavelets in Functional Data Analysis

✍ Scribed by Pedro A. Morettin, Aluísio Pinheiro, Brani Vidakovic/

Publisher
Springer International Publishing
Year
2017
Tongue
English
Leaves
112
Series
SpringerBriefs in Mathematics
Edition
1
Category
Library
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✦ Synopsis

Wavelet-based procedures are key in many areas of statistics, applied mathematics, engineering, and science. This book presents wavelets in functional data analysis, offering a glimpse of problems in which they can be applied, including tumor analysis, functional magnetic resonance and meteorological data. Starting with the Haar wavelet, the authors explore myriad families of wavelets and how they can be used. High-dimensional data visualization (using Andrews' plots), wavelet shrinkage (a simple, yet powerful, procedure for nonparametric models) and a selection of estimation and testing techniques (including a discussion on Stein’s Paradox) make this a highly valuable resource for graduate students and experienced researchers alike.

✦ Table of Contents

Front Matter ....Pages i-viii
Introduction: Examples of Functional Data (Pedro A. Morettin, Aluísio Pinheiro, Brani Vidakovic)....Pages 1-10
Wavelets (Pedro A. Morettin, Aluísio Pinheiro, Brani Vidakovic)....Pages 11-35
Wavelet Shrinkage (Pedro A. Morettin, Aluísio Pinheiro, Brani Vidakovic)....Pages 37-49
Wavelet-Based Andrews’ Plots (Pedro A. Morettin, Aluísio Pinheiro, Brani Vidakovic)....Pages 51-70
Functional ANOVA (Pedro A. Morettin, Aluísio Pinheiro, Brani Vidakovic)....Pages 71-88
Further Topics (Pedro A. Morettin, Aluísio Pinheiro, Brani Vidakovic)....Pages 89-97
Back Matter ....Pages 99-106

✦ Subjects

Functional Analysis

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