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Comments on «Wavelets in statistics: A review» by A. Antoniadis

  • Jianqing Fan
Article

Summary

I would like to congratulate Professor Antoniadis for successfully outlining the current state-of-art of wavelet applications in statistics. Since wavelet techniques were introduced to statistics in the early 90’s, the applications of wavelet techniques have mushroomed. There is a vast forest of wavelet theory and techniques in statistics and one can find himself easily lost in the jungle. The review by Antoniadis, ranging from linear wavelets to nonlinear wavelets, addressing both theoretical issues and practical relevance, gives in-depth coverage of the wavelet applications in statistics and guides one entering easily into the realm of wavelets.

Keywords

Functional Data Analysis Spatial Adaptation Variable Bandwidth Thresholding Function Wavelet Technique 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [1]
    Donoho, D. L., Johnstone, I. M., Hock, J. C. andStern, A. S. (1992). Maximum entropy and the nearly black object (with discussions).Jour. Roy. Statist. Soc. B,54, 41–81.zbMATHGoogle Scholar
  2. [2]
    Fan, J. andGijbels, I. (1995). Data-driven bandwidth selection in local polynomial fitting: variable bandwidth and spatial adaptation.J. Royal Statist. Soc. B,57, 371–394.zbMATHMathSciNetGoogle Scholar
  3. [3]
    Fan, J., Hall, P., Martin, M. andPatil, P. (1999). Adaptation to high spatial inhomogeneity using wavelet methods.Statistica Sinica, 9, 85–102.zbMATHMathSciNetGoogle Scholar
  4. [4]
    Fan, J., Hall, P., Martin, M. andPatil, P. (1996). On the local smoothing of nonparametric curve estimators.J. Amer. Statist. Assoc.,91, 258–266.zbMATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    Fan, J. andLin, S. (1998). Test of significance when data are curves.J. Amer. Statist. Assoc., 93,1007–1021.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    Lepski, O. V., Mammen, E., Spokoiny, V. G. (1997). Optimal spatial adaptation to inhomogeneous smoothness: an approach based on kernel estimates with variable bandwidth selectors.Ann. Statist.,25, 929–947.zbMATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    Ramsay, J. O. andSilverman, B. W. (1997).The analysis of Functional Data. SpringerVerlag, New York.Google Scholar
  8. [8]
    Huber, P. (1981).Robust estimation. New York.Google Scholar
  9. [9]
    Luo, Z. andWahba, G. (1997). Hybrid adaptive splines.Jour. Ameri. Statist. Assoc.,92, 107–116.zbMATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    Tibshrani, R. (1996). Regression shrinkage and selection via lasso.Jour. Roy. Statist. Soc. B.,58, 267–288.Google Scholar

Copyright information

© Società Italiana di Statistica 1997

Authors and Affiliations

  • Jianqing Fan
    • 1
  1. 1.University of North Carolina, Chapel Hill and University of CaliforniaLos Angeles

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