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

Yu-Ye Zou () and Han-Ying Liang ()
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Yu-Ye Zou: Shanghai Maritime University
Han-Ying Liang: Tongji University

Statistical Papers, 2020, vol. 61, issue 6, No 18, 2685-2714

Abstract: Abstract 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.

Keywords: Asymptotic normality; Hellinger distance; Integrated square error; Missing at random; Strong consistency; 62N01; 62G07 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00362-018-01065-9

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