Wavelets in Functional Data Analysis

1. Front Matter

   Pages i-viii

   PDF

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

   PDF

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.

• Nonparametric statistics
• shrinkage
• multiresolution analysis
• high dimension hypotheses testing
• functional statistical modeling
• 62G05
• 62G10
• 62G20
• 42C40

“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)​

• 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

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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