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A Berry-Esseen Type Bound for the Kernel Density Estimator of Length-Biased Data | ||
| Journal of Sciences, Islamic Republic of Iran | ||
| مقاله 6، دوره 26، شماره 3، آذر 2015، صفحه 265-272 اصل مقاله (295.77 K) | ||
| نوع مقاله: Original Paper | ||
| نویسندگان | ||
| P. Asghari؛ V. Fakoor* ؛ M. Sarmad | ||
| Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran. | ||
| چکیده | ||
| Length-biased data are widely seen in applications. They are mostly applicable in epidemiological studies or survival analysis in medical researches. Here we aim to propose a Berry-Esseen type bound for the kernel density estimator of this kind of data.The rate of normal convergence in the proposed Berry-Esseen type theorem is shown to be O(n^(-1/6) ) modulo logarithmic term as n tends to infinity by a proper choice of the bandwidth.The results of a simulation study is also presented in this paper inorder to examine the performance of the result. | ||
| کلیدواژهها | ||
| Asymptotic normality؛ Berry-Esseen theorem؛ Kernel estimator؛ Rate of convergence؛ Length-biased | ||
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