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Fakoor, V.. (1392). Asymptotic Behaviors of Nearest Neighbor Kernel Density Estimator in Left-truncated Data. , 25(1), 57-67.
V. Fakoor. "Asymptotic Behaviors of Nearest Neighbor Kernel Density Estimator in Left-truncated Data". , 25, 1, 1392, 57-67.
Fakoor, V.. (1392). 'Asymptotic Behaviors of Nearest Neighbor Kernel Density Estimator in Left-truncated Data', , 25(1), pp. 57-67.
Fakoor, V.. Asymptotic Behaviors of Nearest Neighbor Kernel Density Estimator in Left-truncated Data. , 1392; 25(1): 57-67.

Asymptotic Behaviors of Nearest Neighbor Kernel Density Estimator in Left-truncated Data

Journal of Sciences, Islamic Republic of Iran
مقاله 7، دوره 25، شماره 1، خرداد 2014، صفحه 57-67    اصل مقاله (755.24 K)
نوع مقاله: Original Paper
نویسنده
V. Fakoor
Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran
چکیده
Kernel density estimators are the basic tools for density estimation in non-parametric statistics.  The k-nearest neighbor kernel estimators represent a special form of kernel density estimators, in  which  the  bandwidth  is varied depending on the location of the sample points. In this paper‎, we  initially introduce the k-nearest neighbor kernel density estimator in the random left-truncation model,  ‎ and then  prove some of its asymptotic behaviors, such as strong uniform consistency and asymptotic normality.  ‎In particular‎, ‎we show that the proposed estimator has truncation-free variance‎. ‎Simulations are presented to illustrate the results and show how the estimator behaves for finite samples‎. Moreover, the proposed estimator is used to estimate  the density function of a real data set.
کلیدواژه‌ها
Asymptotic normality؛ Left-truncation؛ Nearest neighbor؛ Strong consistency
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