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2005 | 25 | 1 | 5-37
Tytuł artykułu

Estimation of the hazard rate function with a reduction of bias and variance at the boundary

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EN
Abstrakty
EN
In the article, we propose a new estimator of the hazard rate function in the framework of the multiplicative point process intensity model. The technique combines the reflection method and the method of transformation. The new method eliminates the boundary effect for suitably selected transformations reducing the bias at the boundary and keeping the asymptotics of the variance. The transformation depends on a pre-estimate of the logarithmic derivative of the hazard function at the boundary.
Twórcy
  • Institute of Mathematics and Informatics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, PL 50-370 Wrocław, Poland
  • Institute of Mathematics and Informatics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, PL 50-370 Wrocław, Poland
Bibliografia
  • [1] O. Aalen, Nonparametric inference for a family of counting processes, The Annals of Statistics 6 (4) (1978), 701-726.
  • [2] P. Andersen, O. Borgan, R. Gill and N. Keiding, Statistical Models Based on Counting Processes, Springer-Verlag, New York 1993.
  • [3] B. Janiszewska and R. Różański, Transformed diffeomorphic kernel estimation of hazard rate function, Demonstratio Mathematica 34 (2) (2001), 447-460.
  • [4] H. Ramlau-Hansen, Smoothing counting process intensities by means of kernel funcions, The Annals of Statistics 11 (2) (1983), 453-466.
  • [5] S. Saoudi, F. Ghorbel and A. Hillion, Some statistical properties of the kernel-diffeomorphism estimator, Applied Stochastic Models and Data Analysis 13 (1997), 39-58.
  • [6] D. Ruppert and J.S. Marron, Transformations to reduce boundary bias in kernel density estimation, J. Roy. Statist. Soc. Ser. B, 56 (4) (1994), 653-671.
  • [7] E.F. Schuster, Incorporating support constraints into nonparametric estimators of densities, Comm. Statist. A - Theory Methods. 14 (1985), 1125-1136.
  • [8] R.S. Liptser and A.N. Shiryayev, Statistics of Random Processes I. General Theory, Springer-Verlag, New York (1984) p. 17.
  • [9] M. Wand, J.S. Marron and D. Ruppert, Transformations in density estimation (with discussion), J. Amer. Statist. Assoc. 86 (1991), 343-361.
  • [10] S. Zhang, R.J. Karunamuni and M.C. Jones, An improved estimator of the density function at the boundary, J. Amer. Statist. Assoc. 94 (1999), 1231-1240.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1058
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