A Review on Nonparametric Density Estimation Using Wavelet Methods

  • Sungho (Professor, Department of Statistics, Taegu University) ;
  • Hwa Rak (Graduate student Department of Statistics Taegu University)
  • Published : 2000.04.01

Abstract

Wavelets constitute a new orthogonal system which has direct application in density estimation. We introduce a brief wavelet density estimation and summarize some asymptotic results. An application to mixture normal distributions is implemented with S-Plus.

Keywords

References

  1. Interpolation Spaces: An introduction Bergh, J.;Lofstrom, J.
  2. Comm. Prre Appl. Math. v.41 Orthogonal bases of compactly supported wavelets Daubechies, I.
  3. Ann. Statist. v.5 Mean intergared squard error properies of density dstimates Davis, K.
  4. Technical Report 403 Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition Donoho, D.L.
  5. Technical Report 402 Minimax estimation via wavelet shrinkage Donoho, D.L.;Johnstone, I.M.
  6. Biometrika v.81 Ideal spatial adaptation by wavelet shrinkage Donoho, D.L.;Johnstone, I.M.
  7. Theory Related Fields v.99 Minimax risk over lp-balls for lq-error. Probab. Donoho, D.L.;Johnstone, I.M.
  8. J. Roy Statist. Soc. Ser. B. v.57 Wavelet shrinkage: asymptopia? (with discussion) Donoho, D.L.;Johnstone, I.M.;Kerkyacharian, G.;Picard, D.
  9. Ann. Statist. v.24 Density estimation by wavelet thresholding Donoho, D.L.;Johnstone, I.M.;Kerkyacharian, G.;Picard, D.
  10. C.R. Acad. Sci. Paris Ser. I Math v.310 Deviation quadratique d'estimateurs d'une densite par projection orthogonale Doukhan, P.;Leon, J.
  11. Studia Sci. Math. Hungar. v.9 A general method of density estimation Foldes, A.;Revez, P.
  12. Ann. Stat. v.23 Formulae for mean integrated squared error of nonlinear wavelet-based density estimators Hall, Peter;Patil, Prakash
  13. Lecture Notes in Statistics 129 Wavelets, Approximation, and Statistical Applications Hardle, W.(et al.)
  14. Statist. Probab. Lett. v.13 Density estimation in Besov spaces Kerkyacharian, G.;Picard, D.
  15. Statist. Probab. Lett. v.18 Density estimation by kernel and wavelet methods: Optimality in Besov spaces Kerkyacharian, G.;Picard, D.
  16. Bernoulli v.2 $L^p$ adaptive density estimation Kerkyacharian, G.;Picard, D.;Triboully, K.
  17. J. Amer. Statist. Assoc. v.63 The estimation of probability densities and cumulative by fourier series methods Kronmal, R.;Tarter, M.
  18. A Study on Wavelet Density Estimation Lee, H.
  19. Wavelets and Operators Meyer, Y.
  20. Ann. Math. Statist. v.33 On estimation of a probability density function and mode Parzen, E.
  21. Nonpara. Statist. v.7 On non-negative wavelet-based density estimatots Penev, S.;Dechevsky, L.
  22. Computational Statistics and Data Analysis v.25 Estimating the square root of a density via compactly Supporter Wavelets Pinheiro, A.;Vidakovic, B.
  23. Ann. Math. Statist. v.27 Remark on some nonparametric estimates of a density function Rosenblatt, M.
  24. Nonparametric density estimation using wavelets, DP 95-26, ISDS Vannucci, M.
  25. Statistical Modeling by Wavelets Vidakovic, B.
  26. Ann. Statist. v.3 Interpolating spline methods for density estimation I. equi-spaced knots Wahba, G.
  27. J. Approx. Theory. v.71 Approximation of the delta function by wavelets Water, G.
  28. Wavelets and Other Orthogonal Systems with Applications Walter, G.