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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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