Skip to main content

Introduction: Examples of Functional Data

  • Chapter
  • First Online:
Wavelets in Functional Data Analysis

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

  • 2057 Accesses

Abstract

Wavelet-based functional data analysis (FDA) is a modern approach to dealing with statistical inference when observations are curves or images. Making inference (estimation and testing) in the wavelet domain is beneficial in several respects such as: reduction of dimensionality, decorrelation, localization, and regularization. This chapter gives an overview of theory for wavelet-based functional analysis, reviews relevant references, and provides some examples that will be used in the next chapters.

As can be seen even by this limited number of examples proteins carry out amazingly diverse functions.

Michael Behe

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Bibliography

  • P.J. Brown, T. Fearn, M. Vannucci, Bayesian wavelet regression on curves with application to a spectroscopic calibration problem. J. Am. Stat. Assoc. 96, 398–408 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  • B. Brumback, J.A. Rice, Smoothing spline models for the analysis of nested and crossed samples of curves. J. Am. Stat. Assoc. 93, 961–994 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  • V. Cahouët, L. Martin, D. Amarantini, Static optimal estimation of joint accelerations for inverse dynamic problem solution. J. Biomech. 35, 1507–1513 (2002)

    Article  Google Scholar 

  • M.W. Dewhirst, R.D. Braun, J.L. Lanzen, Temporal changes in PO2 of R3230Ac tumors in Fischer-344 rats. Int. J. Radiat. Oncol. Biol. Phys. 42, 723–726 (1998)

    Article  Google Scholar 

  • J. Fan, Test of significance based on wavelet thresholding and Neyman’s truncation. J. Am. Stat. Assoc. 91, 674–688 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  • F. Ferraty, Y. Romain, The Oxford Handbook of Functional Data Analysis (Oxford University Press, New York, 2011)

    MATH  Google Scholar 

  • F. Ferraty, P. Vieu, Nonparametric Functional Data Analysis (Springer, New York, 2006)

    MATH  Google Scholar 

  • J.B. German, M.A. Roberts, S.M. Watkins, Genetics and metabolomics as markers for the interaction of diet and health: lessons from lipids. J. Nutr. 133, 2078S–2083S (2003)

    Google Scholar 

  • J.B. German, D.E. Bauman, D.G. Burrin, M.L. Failla, H.C. Freake, J.C. King, S. Klein, J.A. Milner, G.H. Pelto, K.M. Rasmussen, S.H. Zeisel, Metabolomics in the opening decade of the 21st century: building the roads to individualized health. J. Nutr. 134, 2729–2732 (2004)

    Google Scholar 

  • L. Horváth, P. Kokoszka, Inference for Functional Data with Applications (Springer, New York, 2012)

    Book  MATH  Google Scholar 

  • J.L. Lanzen, R.D. Braun, A.L. Ong, M.W. Dewhirst, Variability in blood flow and po2 in tumors in response to carbogen breathing. Int. J. Radiat. Oncol. Biol. Phys. 42, 855–859 (1998)

    Article  Google Scholar 

  • P. Müller, G. Rosner, L. Inoue, M.W. Dewhirst, A Bayesian model for detecting changes in nonlinear profiles. J. Am. Stat. Assoc. 96, 1215–1222 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  • J.O. Ramsay, B.W. Silverman, Applied Functional Data Analysis (Springer, New York, 2002)

    MATH  Google Scholar 

  • J.O. Ramsay, B.W. Silverman, Functional Data Analysis, 2nd edn. (Springer, New York, 2006)

    MATH  Google Scholar 

  • J.O. Ramsay, G. Hooker, S. Graves, Functional Data Analysis with R and MATLAB (Springer, New York, 2009)

    Book  MATH  Google Scholar 

  • J. Raz, B. Turetsky, Wavelet ANOVA and fMRI, in Wavelet Applications in Signal and Image Processing VII, Proceedings of the SPIE (SPIE, Maui, HI, 1999), pp. 561–570

    Book  Google Scholar 

  • J.R. Sato, M.M. Felix, E. Amaro Jr., D.Y. Takahashi, M.J. Brammer, P.A. Morettin, A method to produce evolving functional connectivity maps during the course of an fMRI experiment using wavelet-based time-varying granger causality. NeuroImage 31, 187–196 (2006)

    Article  Google Scholar 

  • J.R. Sato, P.A. Morettin, P.R. Arantes, E. Amaro Jr., Wavelet based time-varying vector autoregressive models. Comput. Stat. Data Anal. 51, 5847–5866 (2007b)

    Google Scholar 

  • J.R. Sato, D.Y. Takahashi, S.M. Arcuri, K. Sameshima, P.A. Morettin, L.A. Baccala, Frequency domain connectivity identification: an application of partial directed coherence in fMRI. Hum. Brain Mapp. 30, 452–461 (2009)

    Article  Google Scholar 

  • B. Vidakovic, Wavelet-based functional data analysis: theory, applications and ramifications, ed. by T. Kobayashi, in Proceedings of PSFVIP-3 (3rd Pacific Symposium on Flow Visualization and Image Processing), PSFVIP-3, Maui, HI, 2001

    Google Scholar 

  • J.T. Zhang, Analysis of Variance for Functional Data (Chapman & Hall, Boca Raton, FL, 2014)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2017 The Author(s)

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Morettin, P.A., Pinheiro, A., Vidakovic, B. (2017). Introduction: Examples of Functional Data. In: Wavelets in Functional Data Analysis. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-59623-5_1

Download citation

Publish with us

Policies and ethics