Advertisement

Probability Density Functions of the Empirical Wavelet Coefficients of Multidimensional Poisson Intensities

  • José Carlos Simon de Miranda
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

We determine the probability density functions of the empirical wavelet coefficient estimator   =   dNin the wavelet series expansion p=    of non homogeneous multidimensional Poisson processes intensity functions.

Keywords

Probability Density Function Poisson Process Point Process Haar Wavelet Wavelet Expansion 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Timmermann, K. E. and Novak, R. D.: Multiscale Bayesian Estimation of Poisson Intensities. IEEE. 85-90 (1998).Google Scholar
  2. [2]
    Novak, R. D. and Kolaczyk, E. D.: A Multiscale MAP Estimation Method for Poisson Inverse Problems. IEEE 1682-1686 (1998).Google Scholar
  3. [3]
    Heikkinen, J. and Arjas, E.: Non-Parametric Bayesian Estimation of a Spatial Pois-son Intensity. Scand J Statist. 25 435-450 (1998).MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Novak, R. D. and Kolaczyk, E. D.: Multiscale Maximum Penalized Likelihood Esti-mators. IEEE. 156, (2002).Google Scholar
  5. [5]
    Müller, P. and Vidakovic, B.: Bayesian Inference with Wavelets: Density Estimation Journal of computational and Graphical Statistics. 7 (4), 456-468 (1998).Google Scholar
  6. [6]
    Barber, S., Nason, G. P. and Silverman, B. W.: Posterior Probability Intervals for Wavelet Thresholding, J. R. Statist. Soc. B. 64, part2, 189-205 (2002).MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    Kolaczyk, E. D. and Novak, R. D.: Multiscale Likelihood Analysis and Complexity Penalized Estimation The Annals of Statistics. 32 (2), 2004, 500-527 (2004).MATHGoogle Scholar
  8. [8]
    Lam, W. M. and Wornell, G. W.: Multiscale Representation and Estimation of Frac-tal Point Processes IEEE Transactions on Signal Processing. 43 (11), 2606-2617 (1995).Google Scholar
  9. [9]
    Winter, A., Maître, H., Cambou, N. and Legrand, E.: Object Detection Using A Multiscale Probability Model IEEE. 269-272 (1996).Google Scholar
  10. [10]
    Figueiredo, M. A. T. and Novak, R. O.: Wavelet-Based Image Estimation: An Em-pirical Bayes Approach Using Je rey's Noninformative Prior. IEEE Transaction on Image Processing. 10 (9), September, 1322-1331 (2001).MATHCrossRefGoogle Scholar
  11. [11]
    Miranda, J.C.S. and Morettin, P.A.: Estimation of the Density of Point Processes on Rm via Wavelets, Technical Report -Department of Mathematics -IME-USP. No. 09, June, 2005.Google Scholar
  12. [12]
    Miranda, J.C.S.: Sobre a estimação da intensidade dos processos pontuais via on-daletas. São Paulo. 92 p. Tese de Doutorado. Instituto de Matemática e Estatística da Universidade de São Paulo. (2003).Google Scholar
  13. [13]
    Miranda, J.C.S. and Morettin, P.A.: On the Estimation of the Intensity of Point Processes on via Wavelets, Technical Report -Department of Statistics -IME-USP. 6,(2006).Google Scholar
  14. [14]
    De Miranda, J.C.S.: Adaptive Maximum Probability Estimation of Multidimensional Poisson Processes Intensity Function. Technical Report -Department of Mathematics -IME-USP. 01, March. (2006).Google Scholar
  15. [15]
    Meyer, Y.: Wavelets and Operators, Cambridge Studies in Advanced Mathematics, 37, April. (1993).Google Scholar
  16. [16]
    Daubechies, I.: Ten Lectures on Wavelets, Philadelphia, P.A. Society for Industrial and Applied Mathematics (CBMS -NSF Regional Conference Series in Applied Mathematics) 61 (1992).Google Scholar
  17. [17]
    Donoho, D. L., Johnstone, I. M.: Ideal Spatial Adaptation by Wavelet Shrinkage Biometrika. 81 (3), 425-455 (1994).MATHMathSciNetGoogle Scholar
  18. [18]
    Donoho, D. L., Johnstone, I. M. Kerkyacharian, G. and Picard, D. : Wavelet Shrink-age: Asymptopia. J. R. Statist. Soc. B. 57 (2), 301-369 (1995).MATHMathSciNetGoogle Scholar
  19. [19]
    Donoho, D. L., Johnstone, I. M. I. M., Kerkyacharian, G. and D. Picard: Density Es-timation by Wavelet Thresholding. The Annals of Statistics. 24 (2), 508-539 (1996).MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Physica-Verlag Heidelberg 2008

Authors and Affiliations

  • José Carlos Simon de Miranda
    • 1
  1. 1.University of São PauloBrazil

Personalised recommendations