Gamma Kernel Estimators for Density and Hazard Rate of Right-Censored Data
The nonparametric estimation for the density and hazard rate functions for right-censored data using the kernel smoothing techniques is considered. The “classical” fixed symmetric kernel type estimator of these functions performs well in the interior region, but it suffers from the problem of bias i...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2011/937574 |
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| author | T. Bouezmarni A. El Ghouch M. Mesfioui |
| author_facet | T. Bouezmarni A. El Ghouch M. Mesfioui |
| author_sort | T. Bouezmarni |
| collection | DOAJ |
| description | The nonparametric estimation for the density and hazard rate functions for right-censored data using the kernel smoothing techniques is considered. The “classical” fixed symmetric kernel type estimator of these functions performs well in the interior region, but it suffers from the problem of bias in the boundary region. Here, we propose new estimators based on the gamma kernels for the density and the hazard rate functions. The estimators are free of bias and achieve the optimal rate of convergence in terms of integrated mean squared error. The mean integrated squared error, the asymptotic normality, and the law of iterated logarithm are studied. A comparison of gamma estimators with the local linear estimator for the density function and with hazard rate estimator proposed by Müller and Wang (1994), which are free from boundary bias, is investigated by simulations. |
| format | Article |
| id | doaj-art-2c2973797ade4e1a8c511f48e955dbf2 |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-2c2973797ade4e1a8c511f48e955dbf22025-02-03T05:51:54ZengWileyJournal of Probability and Statistics1687-952X1687-95382011-01-01201110.1155/2011/937574937574Gamma Kernel Estimators for Density and Hazard Rate of Right-Censored DataT. Bouezmarni0A. El Ghouch1M. Mesfioui2Département de Mathématiques, Université de Sherbrooke, Québec, QC, JIK 2RI, CanadaInstitut de Statistique, Biostatistique et Sciences Actuarielles, Université Catholique de Louvain, 1348 Louvain-La-Neuve, BelgiumDépartement de Mathémathique et d'Informatique, Université du Québec à Trois Rivières, Trois Rivières, QC, G9A 5H7, CanadaThe nonparametric estimation for the density and hazard rate functions for right-censored data using the kernel smoothing techniques is considered. The “classical” fixed symmetric kernel type estimator of these functions performs well in the interior region, but it suffers from the problem of bias in the boundary region. Here, we propose new estimators based on the gamma kernels for the density and the hazard rate functions. The estimators are free of bias and achieve the optimal rate of convergence in terms of integrated mean squared error. The mean integrated squared error, the asymptotic normality, and the law of iterated logarithm are studied. A comparison of gamma estimators with the local linear estimator for the density function and with hazard rate estimator proposed by Müller and Wang (1994), which are free from boundary bias, is investigated by simulations.http://dx.doi.org/10.1155/2011/937574 |
| spellingShingle | T. Bouezmarni A. El Ghouch M. Mesfioui Gamma Kernel Estimators for Density and Hazard Rate of Right-Censored Data Journal of Probability and Statistics |
| title | Gamma Kernel Estimators for Density and Hazard Rate of Right-Censored Data |
| title_full | Gamma Kernel Estimators for Density and Hazard Rate of Right-Censored Data |
| title_fullStr | Gamma Kernel Estimators for Density and Hazard Rate of Right-Censored Data |
| title_full_unstemmed | Gamma Kernel Estimators for Density and Hazard Rate of Right-Censored Data |
| title_short | Gamma Kernel Estimators for Density and Hazard Rate of Right-Censored Data |
| title_sort | gamma kernel estimators for density and hazard rate of right censored data |
| url | http://dx.doi.org/10.1155/2011/937574 |
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