The generalised MLE with truncated interval-censored data

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Nonparametric Statistics Pub Date : 2022-11-22 DOI:10.1080/10485252.2022.2147173

Qiqing Yu

引用次数: 0

Abstract

The generalised maximum likelihood estimator (GMLE) of a survival function based on truncated interval-censored (TIC) data has been studied since 1990s (by Frydman, H. (1994), ‘A note on nonparametric estimation of the distribution function from interval censored and truncated data’, Journal of the Royal Statistical Society, Series B, 56, 71–74 among others). In the literature related to the GMLE based on TIC data, there are several issues that have not been properly settled in both methodology and theory including: (1) innermost intervals based on the TIC data are not correctly formulated and they lead to inconsistent estimators which are not the GMLE; and (2) the consistency of the GMLE has not been established. We settle these two issues in this paper. In particular, we specify the correct forms of innermost intervals and establish consistency results for the GMLE under a realistic model.

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截断间隔截尾数据的广义MLE

自20世纪90年代以来，基于截断区间截短(TIC)数据的生存函数的广义最大似然估计量(GMLE)已经被研究过(由Frydman, H.(1994)，“关于区间截短和截断数据的分布函数的非参数估计的注释”，《皇家统计学会杂志》，B辑，56,71 - 74等)。在基于TIC数据的GMLE相关文献中，有几个问题在方法和理论上都没有得到很好的解决，包括:(1)基于TIC数据的最内层区间没有正确地表述，导致估计量不一致，这不是GMLE;(2) GMLE的一致性尚未建立。本文解决了这两个问题。特别地，我们指定了最内层区间的正确形式，并建立了实际模型下GMLE的一致性结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Nonparametric Statistics 数学-统计学与概率论

CiteScore

1.50

自引率

8.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Journal of Nonparametric Statistics provides a medium for the publication of research and survey work in nonparametric statistics and related areas. The scope includes, but is not limited to the following topics: Nonparametric modeling, Nonparametric function estimation, Rank and other robust and distribution-free procedures, Resampling methods, Lack-of-fit testing, Multivariate analysis, Inference with high-dimensional data, Dimension reduction and variable selection, Methods for errors in variables, missing, censored, and other incomplete data structures, Inference of stochastic processes, Sample surveys, Time series analysis, Longitudinal and functional data analysis, Nonparametric Bayes methods and decision procedures, Semiparametric models and procedures, Statistical methods for imaging and tomography, Statistical inverse problems, Financial statistics and econometrics, Bioinformatics and comparative genomics, Statistical algorithms and machine learning. Both the theory and applications of nonparametric statistics are covered in the journal. Research applying nonparametric methods to medicine, engineering, technology, science and humanities is welcomed, provided the novelty and quality level are of the highest order. Authors are encouraged to submit supplementary technical arguments, computer code, data analysed in the paper or any additional information for online publication along with the published paper.