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Asghari, P., Fakoor, V., Sarmad, M.. (1394). A Berry-Esseen Type Bound for the Kernel Density Estimator of Length-Biased Data. , 26(3), 265-272.
P. Asghari; V. Fakoor; M. Sarmad. "A Berry-Esseen Type Bound for the Kernel Density Estimator of Length-Biased Data". , 26, 3, 1394, 265-272.
Asghari, P., Fakoor, V., Sarmad, M.. (1394). 'A Berry-Esseen Type Bound for the Kernel Density Estimator of Length-Biased Data', , 26(3), pp. 265-272.
Asghari, P., Fakoor, V., Sarmad, M.. A Berry-Esseen Type Bound for the Kernel Density Estimator of Length-Biased Data. , 1394; 26(3): 265-272.

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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