Journal of the Korean Statistical Society

  • 제31권3호
  • /
  • Pages.343-357
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  • 2002
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  • 1226-3192(pISSN)
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  • 2005-2863(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

Inhomogeneous Poisson Intensity Estimation via Information Projections onto Wavelet Subspaces

  • Kim, Woo-Chul (Department of Statistics, Seoul National University) ;
  • Koo, Ja-Yong (Department of Statistics, Inha University)
  • 발행 : 2002.09.01
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초록

This paper proposes a method for producing smooth and positive estimates of the intensity function of an inhomogeneous Poisson process based on the shrinkage of wavelet coefficients of the observed counts. The information projection is used in conjunction with the level-dependent thresholds to yield smooth and positive estimates. This work is motivated by and demonstrated within the context of a problem involving gamma-ray burst data in astronomy. Simulation results are also presented in order to show the performance of the information projection estimators.

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참고문헌

  1. Journal of Statistical Planning and Inference v.50 Spatial point processes in Astronomy Babu, G.J.;Feigelson, E. https://doi.org/10.1016/0378-3758(95)00060-7
  2. The Annals of Statistics v.19 Approsimations of density functions by sequences of exponetial families Barron, A.R.;Sheu, C.-H. https://doi.org/10.1214/aos/1176348252
  3. Applied Computational and Harmonic Analysis v.1 Wavelets on the interval and fast wavelet transforms Cohen, A.;Daubechies, I.;Vial, P. https://doi.org/10.1006/acha.1993.1005
  4. Journal of the American Statistical Association v.91 Bootstrap confidence regions for the intensity of a Poisson point process Cowling, A.;Hall, P.;Phillips, J.P. https://doi.org/10.2307/2291577
  5. SIAM Journal of Mathematical Analysis v.24 Orthonormal bases of compactly supported wavelets Ⅱ: variations on a theme Daubechies, I. https://doi.org/10.1137/0524031
  6. Applied Statistics v.34 A kernel method for smoothing point process data Diggle, P. https://doi.org/10.2307/2347366
  7. Journal of the American Statistical Association v.83 Equivalence of smoothing parameter selectors in density and intensity estimation Diggle, P.;Marron, J.S. https://doi.org/10.2307/2289308
  8. Wavelets and Statistics Translation-invariant de-noising Donobo, D.L.;Coifman, R.R.;A. Antoniadis(eds.);G. Oppenheim(eds.)
  9. Biometrika v.81 Ideal spatial adaptation via wavelet shrinkage Donoho, D.L.;Johnstone, I.M. https://doi.org/10.1093/biomet/81.3.425
  10. The Annals of Statistics v.26 Minimax estimation via wavelet shrinkage Donoho, D.L.;Johnstone, I.M. https://doi.org/10.1214/aos/1024691081
  11. Journal of the Royal Statististical Society v.B57 Wavelet Shrinkage: asymptopia? Donoho, D.L.;Johnstone, I.M.;Kerkyacharian, G.;Picard, D.
  12. Advanced Applied Probability v.18 A limit theorem for spatial point processes Ellis, S.P.
  13. Astrophysical Journal v.483 Non-parametric estimation of gamma-ray burst intensities using Haar wavelets Kolaczyk, E.D. https://doi.org/10.1086/304243
  14. Statistica Sinica v.9 Wavelet shrinkage estimation of certain Poisson intensity signals using corrected thresholds Kolaczyk, E.D.
  15. Nature v.355 The spatial distribution of gamma ray bursts observed by BATSE Meegan, C.A.;Fishman, G.J.;Wilson, R.B.;Paciesas, W.S.;Pendleton, G.N.;Horack, J.M.;Brock, M.N.;Kouveliotou, G. https://doi.org/10.1038/355143a0
  16. Wavelets and Operators Meyer, Y.
  17. Numerical Recipes in C, the Art of Scientific Computing v.2 Press, W.H.;Teukolsky, S.A.;Vetterling, W.T.;Flannery, B.P.