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.

中文翻译：

---

具有随机缺失删失指标的密度估计器的积分平方误差的 CLT

寿命密度与其估计量之间距离的流行随机度量是积分平方误差 (ISE) 和海灵格距离 (HD)。在本文中，我们关注的是当删失指标随机缺失时的右删失模型。基于 Wang 等人定义的两个密度估计量 (J Multivar Anal 100:835–850, 2009) 和另一个新的密度核估计量，我们为建议的估计量建立了 ISE 和 HD 的渐近正态性。此外，讨论了新的密度核估计量的一致强一致性。此外，还进行了模拟研究以比较所提出的估计器的有限样本性能。