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Wavelets in Functional Data Analysis

  • Book
  • © 2017

Overview

Authors:
  1. Pedro A. Morettin

    1. Department of Statistics, University of São Paulo, São Paulo, Brazil

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  2. Aluísio Pinheiro

    1. Department of Statistics, University of Campinas, Campinas, Brazil

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    You can also search for this author in PubMed   Google Scholar

  3. Brani Vidakovic

    1. The Wallace H. Coulter Department of Biomedical Engineering, Georgia Inst Tech & Emory Univ Sch Med, Atlanta, USA

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    You can also search for this author in PubMed   Google Scholar

  • Brings together results in wavelet functional data analysis that to date were only available in papers
  • The only book to present functional data analysis from a wavelet point of view in a general framework
  • Offers numerous sample coded applications for use with MATLAB
  • Includes chapters in state-of-the-art topics like visualization of functional analysis via wavelets, optimal estimation and testing methods

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-viii
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  2. Introduction: Examples of Functional Data

    • Pedro A. Morettin, Aluísio Pinheiro, Brani Vidakovic
    Pages 1-10

  3. Wavelets

    • Pedro A. Morettin, Aluísio Pinheiro, Brani Vidakovic
    Pages 11-35

  4. Wavelet Shrinkage

    • Pedro A. Morettin, Aluísio Pinheiro, Brani Vidakovic
    Pages 37-49

  5. Wavelet-Based Andrews’ Plots

    • Pedro A. Morettin, Aluísio Pinheiro, Brani Vidakovic
    Pages 51-70

  6. Functional ANOVA

    • Pedro A. Morettin, Aluísio Pinheiro, Brani Vidakovic
    Pages 71-88

  7. Further Topics

    • Pedro A. Morettin, Aluísio Pinheiro, Brani Vidakovic
    Pages 89-97

  8. Back Matter

    Pages 99-106
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Keywords

About this book

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.

Reviews

“This book is short and offers quick reference on common techniques for application of wavelets on functional data analysis using some real data examples. The authors have provided code examples in Matlab for some of the methods discussed in this book. … this is a useful book for quick reference for researchers in this field.” (Abhirup Mallik, Technometrics, Vol. 60 (3), 2018)​

Authors and Affiliations

  • Department of Statistics, University of São Paulo, São Paulo, Brazil

    Pedro A. Morettin

  • Department of Statistics, University of Campinas, Campinas, Brazil

    Aluísio Pinheiro

  • The Wallace H. Coulter Department of Biomedical Engineering, Georgia Inst Tech & Emory Univ Sch Med, Atlanta, USA

    Brani Vidakovic

About the authors

Pedro A. Morettin holds a B.S. degree in Mathematics from the University of São Paulo, Brazil, with M.A. and Ph.D. degrees in Statistics from the University of California at Berkeley, USA. He is currently emeritus professor at the University of São Paulo's Statistics Department. His main research areas include nonparametric statistics, particularly with the use of wavelets and applications to finance. He received the Mahalanobis Award from by the Government of India and the International Statistical Institute in 2009, and the Brazilian Statistical Association Award in 2006.


Aluísio Pinheiro holds a B.S. and M.S. in Statistics from National School of Statistical Sciences (ENCE), Brazil, and University of Campinas, respectively. He also has a Ph.D. in Statistics from the University of North Carolina at Chapel Hill, USA. He is currently affiliated to the University of Campinas. His main research areas are nonparametric statistics, estimation and asymptotics, particularly wavelets and U-statistics. In 2012 he was awarded the P. K. Sen Distinguished Visiting Professorship of Biostatistics at the University of North Carolina.


Brani Vidakovic holds a B.S. in Mathematics and a M.S. in Probability from Belgrade University, Serbia, and a Ph.D. in Statistics from Purdue University, USA (1992). He is currently affiliated to Georgia Tech and Emory University, both in the USA. His main research areas are Bayesian modeling, wavelet statistics and multi-scale data analysis. He was the recipient of the 1992 Burr's award for best Ph.D. student at Purdue University. He is an associate editor of several leading statistical journals.



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