Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지

A Note On L$_1$ Strongly Consistent Wavelet Density Estimator for the Deconvolution Problems

  • Lee, Sungho (Professor, Department of Statistics, Taegu University)
  • Published : 2001.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

The problem of wavelet density estimation is studied when the sample observations are contaminated with random noise. In this paper a linear wavelet estimator based on Meyer-type wavelets is shown to be L$_1$ strongly consistent for f(x) with bounded support when Fourier transform of random noise has polynomial descent or exponential descent.

Keywords

References

  1. Journal of the American Statistical Association v.83 Optimal rates convergence for deconvoluting a density Carroll,R.J.;Hall,P.
  2. Ten Lectures on Wavelets CBMS-MSF Daubechies,I.
  3. Journal of the Royal Statistical Society, Series B v.57 Wavelet shrinkage: asymptopia? (with discussion) Donoho,D.;Johnstone,I.;Kerkyacharian,G.;Picard,D.
  4. Annals of Statistics v.24 Density estimation by wavelet thresholding Donoho,D.;Johnstone,I.;Kerkyacharian,G.;Picard,D.
  5. Annals of Statistics v.19 On the optimal rates of convergence for nonparametric deconvolution provlem Fan,J.
  6. The Korean communications in Statistics v.7 A review on nonparametric density estimation using wavelet methods Lee,S.;Lee,H.
  7. Statistics in Medicine v.10 Using empirical Bayes methods in biopharmaceutical research Louis,T.A.
  8. Annals of Statistics v.27 Adaptive wavelet estimator for nonparametric density deconvolution Pensky,M.;Vidakovic,B.
  9. Communications in Statistics: Theory and Methods v.19 On a strongly consistent nonparametric denisty estimator for deconvolution problem Taylor,R.L.;Zhang,H.M.
  10. Statistical Modeling by Wavelets Vidakovic,B.
  11. Wavelets and Other Orthogonal Systems with Applications Walter,G.G.
  12. Statistics & Probability Letters v.41 Density estimation in the presence of noise Walter,G.G.
  13. Statistical Sinica v.2 On deconvolution using time of flight information in positron emission tomography Zhang,H.P.