Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

A Note on Nonparametric Density Estimation for the Deconvolution Problem

  • Published : 2008.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper the support vector method is presented for the probability density function estimation when the sample observations are contaminated with random noise. The performance of the procedure is compared to kernel density estimates by the simulation study.

Keywords

References

  1. Aronszajn, N. (1950). Theory of reproducing kernels, Transactions of the American Mathematical Society, 68, 337-404 https://doi.org/10.2307/1990404
  2. Carroll, R. J. and Hall, P. (1988). Optimal rates of convergence for deconvoluting a density, Journal of the American Statistical Association, 83, 1184-1886 https://doi.org/10.2307/2290153
  3. Fan, J. (1991). On the optimal rates of convergence for nonparametric deconvolution problems, The Annals of Statistics, 19, 1257-1272 https://doi.org/10.1214/aos/1176348248
  4. Gunn, S. R. (1998). Support vector machines for classi¯cation and regression. Technical report. University of Southampton
  5. Lee, S. (2001). A note on strongly consistent wavelet density estimator for the deconvolution problem, The Korean Communications in Statistics, 8, 859-866
  6. Lee, S. (2002). A note on Central limit theorem for deconvolution wavelet density estimator, The Korean Communications in Statistics, 9, 241-248 https://doi.org/10.5351/CKSS.2002.9.1.241
  7. Lee, S. and Hong, D. H. (2002). On a strongly consistent wavelet density estimator for the deconvolution problem, Communications in Statistics - Theory and Methods, 31, 1259-1272 https://doi.org/10.1081/STA-120006067
  8. Lee, S. and Taylor, R. L. (2008). A note on support vector density estimation for the deconvolution problem, Communications in Statistics - Theory and Methods, 37, 328-336 https://doi.org/10.1080/03610920701653086
  9. Liu, M. C. and Taylor, R. L. (1989). A consistent nonparametric density estimator for the deconvolution problem, The Canadian Journal of Statistics, 17, 427-438 https://doi.org/10.2307/3315482
  10. Louis, T. A. (1991). Using empirical Bayes methods in biopharmaceutical research, Statistics in Medicine, 10, 811-827 https://doi.org/10.1002/sim.4780100604
  11. Mukherjee, S. and Vapnik, V. (1999). Support vector method for multivariate density estimation. Technical Report. A.I. Memo no. 1653, MIT AI Lab
  12. Nadaraya, E. (1964). On regression estimators, Theory of Probability and It's Application, 9, 157-159
  13. Pensky, M. and Vidakovic, B. (1999). Adaptive wavelet estimator for nonparametric density deconvolutoin, The Annals of Statistics, 27, 2033-2053 https://doi.org/10.1214/aos/1017939249
  14. Vapnik, V. (1995). The Nature of Statistical Learning Theory, Springer Verlag, New York
  15. Vapnik, V. and Chervonenkis, A. (1964). A note on one class of perceptrons, Automation and Remote Control, 25
  16. Vapnik, V. and Lerner, A. (1963). Pattern recognition using generalized portrait method, Automation and Remote Control, 24
  17. Walter, G. G. (1999). Density estimation in the presence of noise, Statistics & Probability Letters, 41, 237-246 https://doi.org/10.1016/S0167-7152(98)00160-6
  18. Watson, G. S. (1964). Smooth regression analysis, Sankhya: The Indian Journal of Statistics, Ser. A, 26, 359-372
  19. Weston, J., Gammerman, A., Stitson, M., Vapnik, V., Vovk, V. and Watkins, C. (1999). Support vector density estimation, In Scholkopf, B. and Smola, A., editors, Advances in Kernel Methods-Suppot Vector Learning, 293-306, MIT Press, Cambridge, MA
  20. Zhang, H. P. (1992). On deconvolution using time of flight information in positron emission tomography, Statistica Sinica, 2, 553-575