CLT for integrated square error of density estimators with censoring indicators missing at random

  • Yu-Ye Zou
  • Han-Ying LiangEmail author
Regular Article


A popular stochastic measure of the distance between the density of the lifetimes and its estimator is the integrated square error (ISE) and Hellinger distance (HD). In this paper, we focus on the right-censored model when the censoring indicators are missing at random. Based on two density estimators defined by Wang et al.(J Multivar Anal 100:835–850, 2009), and another new kernel estimator of the density, we established the asymptotic normality of the ISE and HD for the proposed estimators. In addition, the uniformly strongly consistency of the new kernel estimator of the density is discussed. Also, a simulation study is conducted to compare finite-sample performance of the proposed estimators.


Asymptotic normality Hellinger distance Integrated square error Missing at random Strong consistency 

Mathematics Subject Classification

62N01 62G07 



The first author was supported by the Major Research Plan of the National Social Science Foundation of China (18ZD05). The second author was supported by the National Natural Science Foundation of China (11671299) and the National Social Science Foundation of China (17BTJ032).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Economics and ManagementShanghai Maritime UniversityShanghaiPeople’s Republic of China
  2. 2.School of Mathematical ScienceTongji UniversityShanghaiPeople’s Republic of China

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