Some Asymptotic Results of Kernel Density Estimator in Length-Biased Sampling - M. Ajami; V. Fakoor; S. Jomhoori (Journal of Sciences, Islamic Republic of Iran)
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.