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

Bożena Janiszewska; Roman Różański

Discussiones Mathematicae Probability and Statistics (2005)

  • Volume: 25, Issue: 1, page 5-37
  • ISSN: 1509-9423

Abstract

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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.

How to cite

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Bożena Janiszewska, and Roman Różański. "Estimation of the hazard rate function with a reduction of bias and variance at the boundary." Discussiones Mathematicae Probability and Statistics 25.1 (2005): 5-37. <http://eudml.org/doc/287673>.

@article{BożenaJaniszewska2005,
abstract = {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.},
author = {Bożena Janiszewska, Roman Różański},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {hazard rate function; multiplicative intensity point process model; Ramlau-Hansen kernel estimator; reduction of the bias; reflection; transformation},
language = {eng},
number = {1},
pages = {5-37},
title = {Estimation of the hazard rate function with a reduction of bias and variance at the boundary},
url = {http://eudml.org/doc/287673},
volume = {25},
year = {2005},
}

TY - JOUR
AU - Bożena Janiszewska
AU - Roman Różański
TI - Estimation of the hazard rate function with a reduction of bias and variance at the boundary
JO - Discussiones Mathematicae Probability and Statistics
PY - 2005
VL - 25
IS - 1
SP - 5
EP - 37
AB - 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.
LA - eng
KW - hazard rate function; multiplicative intensity point process model; Ramlau-Hansen kernel estimator; reduction of the bias; reflection; transformation
UR - http://eudml.org/doc/287673
ER -

References

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  1. [1] O. Aalen, Nonparametric inference for a family of counting processes, The Annals of Statistics 6 (4) (1978), 701-726. Zbl0389.62025
  2. [2] P. Andersen, O. Borgan, R. Gill and N. Keiding, Statistical Models Based on Counting Processes, Springer-Verlag, New York 1993. Zbl0769.62061
  3. [3] B. Janiszewska and R. Różański, Transformed diffeomorphic kernel estimation of hazard rate function, Demonstratio Mathematica 34 (2) (2001), 447-460. Zbl0999.62029
  4. [4] H. Ramlau-Hansen, Smoothing counting process intensities by means of kernel funcions, The Annals of Statistics 11 (2) (1983), 453-466. 
  5. [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. Zbl0924.62034
  6. [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. Zbl0805.62046
  7. [7] E.F. Schuster, Incorporating support constraints into nonparametric estimators of densities, Comm. Statist. A - Theory Methods. 14 (1985), 1125-1136. 
  8. [8] R.S. Liptser and A.N. Shiryayev, Statistics of Random Processes I. General Theory, Springer-Verlag, New York (1984) p. 17. Zbl0364.60004
  9. [9] M. Wand, J.S. Marron and D. Ruppert, Transformations in density estimation (with discussion), J. Amer. Statist. Assoc. 86 (1991), 343-361. Zbl0742.62046
  10. [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. Zbl0994.62029

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