Document Type : Original Paper

Authors

• M. Ajami ¹
• V. Fakoor ¹
• S. Jomhoori ²

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.

Keywords

• Asymptotic normality
• Length-biased
• Strong consistency
• Strong Gaussian approximation