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Abstrakty
In the article, a transformed diffeomorphic kernel estimator of the hazard rate function in the presence of censoring is constructed. The estimator is defined in the framework of multiplicative intensity point process model. It is shown that the proposed estimator is asymptotically unbiased, consistent and asymptotically normal. Analysis in the reduction of the bias of the diffeomorphic estimator is carried out. Some simulation results comparing the obtained estimator with the Ramlau-Hansen estimator are also presented.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Strony
447--460
Opis fizyczny
Bibliogr. 13 poz.
Twórcy
autor
- Institute of Mathematics Wrocław University of Technology ul. Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland
autor
- Institute of Mathematics Wrocław University of Technology ul. Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland
Bibliografia
- [1] O. Aalen, (1978). Nonparametric inference for a family of counting processes, Arm. Statist. 6(4), 701-726.
- [2] P. Andersen, O. Borgan, R. Gill, and N. Keiding, (1993). Statistical Models Based on Counting Processes. Springer-Verlag, New York.
- [3] P. K. Andersen and O. Borgan, (1985). Counting process models for life history, Scand. J. Statist, 12, 97-158.
- [4] M. Y. Cheng, J. Fan, and J. S. Marron, (1997) On automatic boundary corrections, Ann. Statistics, 25, 1691-1.
- [5] D. B. H. Cline, and J. D. Hart, (1991) Kernel estimation of densities with discontinuities or discontinuous derivatives, Statistics, 22, 69-84.
- [6] T. R. Fleming, and D. P. Harrington, (1991) Counting Processes and Survival Analysis, John Wiley Si Sons.
- [7] H. Ramlau-Hansen, (1983). Smoothing counting process intensities by means of kernel funcions, Ann. Statist., 11(2), 453-466.
- [8] R. Rebolledo, (1980). Central limit theorems for local martingales, Z. Wahrsch. Verw. Gebiete, 51, 269-286.
- [9] S. Saoudi, F. Ghorbel, and A. Hillion, (1997) Some statistical properties of the kernel-diffeomorphism estimator, App. Stochastic Models Data Anal., Vol. 13, 39-58.
- [10] D. Ruppert, and J. S. Marron, (1994) Transformations to reduce boundary bias in kernel density estimation, J. Roy. Statist. Soc. Ser. B, 56(4), 653-671.
- [11] E. F. Schuster, (1985) Incorporating support constraints into nonparametric estimators of densities, Comm. Statist. A - Theory Methods., 14, 1125-1136.
- [12] M. Wand, J. S. Marron, D. Ruppert, (1991) Transformations in density estimation (with discussion), J. Amer. Statist. Assoc., 86, 343-361.
- [13] S. Zhang, R. J. Karunamuni, and M. C. Jones, (1999) An improved estimator of the density function at the boundary, J. Amer. Statist. Assoc., 94, 1231-1240.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA1-0039-0010