Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran
Abstract
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.
Fakoor,V . (2014). Asymptotic Behaviors of Nearest Neighbor Kernel Density Estimator in Left-truncated Data. Journal of Sciences, Islamic Republic of Iran, 25(1), 57-67.
MLA
Fakoor,V . "Asymptotic Behaviors of Nearest Neighbor Kernel Density Estimator in Left-truncated Data", Journal of Sciences, Islamic Republic of Iran, 25, 1, 2014, 57-67.
HARVARD
Fakoor V. (2014). 'Asymptotic Behaviors of Nearest Neighbor Kernel Density Estimator in Left-truncated Data', Journal of Sciences, Islamic Republic of Iran, 25(1), pp. 57-67.
CHICAGO
V Fakoor, "Asymptotic Behaviors of Nearest Neighbor Kernel Density Estimator in Left-truncated Data," Journal of Sciences, Islamic Republic of Iran, 25 1 (2014): 57-67,
VANCOUVER
Fakoor V. Asymptotic Behaviors of Nearest Neighbor Kernel Density Estimator in Left-truncated Data. J. Sci. I. R. I.. 2014;25(1):57-67.
Journal of Sciences, Islamic Republic of Iran