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Ajami, M., Fakoor, V., Jomhoori, S.. (1391). Some Asymptotic Results of Kernel Density Estimator in Length-Biased Sampling. , 24(1), 55-62.
M. Ajami; V. Fakoor; S. Jomhoori. "Some Asymptotic Results of Kernel Density Estimator in Length-Biased Sampling". , 24, 1, 1391, 55-62.
Ajami, M., Fakoor, V., Jomhoori, S.. (1391). 'Some Asymptotic Results of Kernel Density Estimator in Length-Biased Sampling', , 24(1), pp. 55-62.
Ajami, M., Fakoor, V., Jomhoori, S.. Some Asymptotic Results of Kernel Density Estimator in Length-Biased Sampling. , 1391; 24(1): 55-62.

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

Journal of Sciences, Islamic Republic of Iran
مقاله 5، دوره 24، شماره 1، خرداد 2013، صفحه 55-62    اصل مقاله (534.7 K)
نوع مقاله: Original Paper
نویسندگان
M. Ajami1؛ V. Fakoor1؛ S. Jomhoori2
1Department of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran
2Department of Statistics, Faculty of Sciences, University of Birjand, Birjand, Islamic Republic of Iran
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
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