Some Asymptotic Results of Kernel Density Estimator in Length-Biased Sampling

نویسندگان
Ajami, M. ID 1
Fakoor, V. ID 2
Jomhoori, S. ID 3

1 Department of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran

2 Department of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran

3 Department of Statistics, Faculty of Sciences, University of Birjand, Birjand, Islamic Republic of Iran

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چکیده

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.

کلیدواژه‌ها
Asymptotic normality, Length-biased, Strong consistency, Strong Gaussian approximation