Communications for Statistical Applications and Methods

  • 제4권3호
  • /
  • Pages.833-845
  • /
  • 1997
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  • 2287-7843(pISSN)
  • /
  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

A Study of Log-Fourier Deconvolution

  • Ja Yong Koo (Department of Statistics, Hallym University, Chunchon, 200-702, Korea) ;
  • Hyun Suk Park (Candidate of Ph. D., Department of Statistics, Hallym University, Chunchon, 200-702, Korea)
  • 발행 : 1997.12.01
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초록

Fourier expansion is considered for the deconvolution problem of estimating a probability density function when the sample observations are contaminated with random noise. In the log-Fourier method of density estimation for data without noise, the logarithm of the unknown density function is approximated by a trigonometric function, the unknown parameters of which are estimated by maximum likelihood. The log-Fourier density estimation method, which has been considered theoretically by Koo and Chung (1997), is studied for the finite-sample case with noise. Numerical examples using simulated data are given to show the performance of the log-Fourier deconvolution.

키워드

참고문헌

  1. The Annals of Statistics v.19 Approximation of density functions by sequences of exponential families Barron, A. R.;Sheu, C. -H.
  2. A Practical Guide to Splines de Boor, C.
  3. Journal of the American Statistical Association v.83 Optimal rates of convergence for deconvolving a density Carroll, R. J.;Hall, P.
  4. Nonparametric Density Estimation : The L₁view Devroye, L.;Grorfi, L.
  5. The Annals of Statistics v.19 On the optimal rate of convergence for nonparametric deconvolution problems Fan, J.
  6. Measurement Error Models Fuller, W. A.
  7. The Annals of Statistics v.21 Optimal rates of convergence for nonparametric statistical inverse problems Koo, J. -Y.
  8. Computational Statistics and Data Analysis v.21 Bivariate B-splines for tensor logspline density estimation Koo, J. -Y.
  9. The Annals of Statistics Log-density estimation in linear inverse problems Koo, J. -Y.;Chung, H. -Y.
  10. Statistics and Probability Letters v.26 Wavelet density estimation by approximation of log-densities Koo, J. -Y.;Kim, W. -C.
  11. Journal of statistical Computation and Simulation v.54 B-spline deconvolution based on the EM algorithm Koo, J. -Y.;Park, B. U.
  12. The Korean Journal of Applied statistics v.10 Log-density estimation based on the Fourier expansion Koo, J. -Y.;Lee, K. -W.;Park, H. -S.
  13. Computational Statistics and Data Analysis v.12 A study of logspline density estimation Kooperberg, C.;Stone, C. J.
  14. Journal of Computational and Graphical Statistics v.1 Logspline density estimation for censored data Kooperberg, C.;Stone, C. J.
  15. Canadian Journal of Statistics v.17 A consistent nonparametric density estimator for the deconvolution problem Liu, M. C.;Taylor, R. L.
  16. Journal of the American Statistical Association v.77 Deconvolution of microfluorometric histograms with B-splines Mendelsohn, J.;Rice, J.
  17. Numerical Recipes in FORTRAN(2nd edition) Press, W. H.;Teukolsky, S. A.;Vetterling, W. T.;Flannery, B. P.
  18. Density Estimation for Statistics and Data Analysis Silverman, B. W.
  19. Journal of Royal Statistical Society. Series B v.52 A smoothed EM algorithm to indirect estimation problems, with particular reference to stereology and emission tomography Silverman, B. W.;Jones, M. C.;Nychka, D. W.;Wilson, J. D.
  20. Statistics v.21 Deconvoluting kernel density estimators Stefanski, L.;Carroll, R. J.
  21. The Annals of Statistics v.18 Large sample inference for logspline model Stone, C. J.
  22. Contemporary Mathematics v.59 Logspline density estimation Stone, C. J.;Koo, C. -Y.
  23. Journal of Royal Statistical Society. Series B v.55 From image deblurring to optimal investments: Maximum likelihood solutions for positive linear inverse problems Vardi, Y.;Lee, D.
  24. The Annals of Statistics v.18 Fourier methods for estimating mixing densities and distributions Zhang, C. H.