1
Department of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran
2
Department of Statistics, Faculty of Sciences, University of Birjand, Birjand, Islamic Republic of Iran
Abstract
In this paper, we prove the strong uniform consistency and asymptotic normality of the kernel density estimator proposed by Jones [12] for length-biased data.The approach is based on the invariance principle for the empirical processes proved by Horváth [10]. All simulations are drawn for different cases to demonstrate both, consistency and asymptotic normality and the method is illustrated by real automobile brake pads data.
Ajami,M , Fakoor,V and Jomhoori,S . (2013). Some Asymptotic Results of Kernel Density
Estimator in Length-Biased Sampling. Journal of Sciences, Islamic Republic of Iran, 24(1), 55-62.
MLA
Ajami,M , , Fakoor,V , and Jomhoori,S . "Some Asymptotic Results of Kernel Density
Estimator in Length-Biased Sampling", Journal of Sciences, Islamic Republic of Iran, 24, 1, 2013, 55-62.
HARVARD
Ajami M, Fakoor V, Jomhoori S. (2013). 'Some Asymptotic Results of Kernel Density
Estimator in Length-Biased Sampling', Journal of Sciences, Islamic Republic of Iran, 24(1), pp. 55-62.
CHICAGO
M Ajami, V Fakoor and S Jomhoori, "Some Asymptotic Results of Kernel Density
Estimator in Length-Biased Sampling," Journal of Sciences, Islamic Republic of Iran, 24 1 (2013): 55-62,
VANCOUVER
Ajami M, Fakoor V, Jomhoori S. Some Asymptotic Results of Kernel Density
Estimator in Length-Biased Sampling. J. Sci. I. R. I.. 2013;24(1):55-62.
Journal of Sciences, Islamic Republic of Iran