A maximum smoothed likelihood estimator in the current status continuous mark model

Piet Groeneboom; Geurt Jongbloed; Birgit I. Witte

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A maximum smoothed likelihood estimator in the current status continuous mark model

机译：当前状态连续标记模型中的最大平滑似然估计

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摘要

We consider the problem of estimating the joint distribution function of the event time and a continuous mark variable based on censored data. More specifically, the event time is subject to current status censoring and the continuous mark is only observed in case inspection takes place after the event time. The nonpara-metric maximum likelihood estimator in this model is known to be inconsistent. We propose and study an alternative likelihood-based estimator, maximising a smoothed log-likelihood, hence called a maximum smoothed likelihood estimator (MSLE). This estimator is shown to be well defined and consistent, and a simple algorithm is described that can be used to compute it. The MSLE is compared with other estimators in a small simulation study.

机译：我们考虑了基于审查数据估计事件时间和连续标记变量的联合分布函数的问题。更具体地说，事件时间受当前状态检查，并且仅在事件时间之后进行检查的情况下才观察到连续标记。已知该模型中的非参数最大似然估计是不一致的。我们提出并研究了一种替代的基于似然性的估计器，它使平滑的对数似然性最大化，因此称为最大平滑似然估计器（MSLE）。该估计器显示出定义良好且一致的特点，并描述了一种可用于计算它的简单算法。在一个小型模拟研究中，MSLE与其他估计量进行了比较。

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来源
《Journal of nonparametric statistics》 |2012年第2期|p.85-101|共17页
作者
Piet Groeneboom; Geurt Jongbloed; Birgit I. Witte;
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作者单位

Delft Institute of Applied Mathematics, Delft Univerisity of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands;

Delft Institute of Applied Mathematics, Delft Univerisity of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands;

Department of Epidemiology and Biostatistics, VU University Medical Center, PO Box 7057, 1007 MB Amsterdam, The Netherlands;

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正文语种 eng
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关键词
bivariate distribution function; censored data; pointwise consistency; histogram estimator; kullback-leibler divergence;

机译：二元分布函数审查数据;点状一致性直方图估计器Kullback-Leibler散度;

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1. Smooth Plug-in Inverse Estimators in the Current Status Continuous Mark Model [J] . PIET GROENEBOOM, GEURT JONGBLOED, BIRGIT I. WITTE Scandinavian journal of statistics . 2012,第1期

机译：当前状态连续标记模型中的平滑插件逆估计
2. The nonparametric maximum likelihood estimator in a class of doubly censored current status data models with application to partner studies [J] . Van Der Laan MJ., Andrews C. Biometrika . 2000,第1期

机译：一类双重审查的当前状态数据模型中的非参数最大似然估计及其在伙伴研究中的应用
3. MAXIMUM SMOOTHED LIKELIHOOD ESTIMATION ANDSMOOTHED MAXIMUM LIKELIHOOD ESTIMATION IN THECURRENT STATUS MODEL [J] . BY PIET GROENEBOOM, GEURT JONGBLOED, BIRGIT I. WITTE The Annals of Statistics: An Official Journal of the Institute of Mathematical Statistics . 2010,第1期

机译：当前状态模型中最大平稳似然估计中的最大平稳似然估计
4. Asymptotic study of the maximum likelihood estimator of a change-point under smooth changes in multivariate Gaussian families [C] . Stergios Fotopoulos, Li Tan, Venkata Jandhyala Decision Sciences Institute Annual Meeting . 2007

机译：多元高斯族平稳变化下变化点最大似然估计的渐近研究
5. A comparison of estimators in hierarchical linear modeling: Restricted maximum likelihood versus bootstrap via minimum norm quadratic unbiased estimators. [D] . Delpish, Ayesha Nneka. 2006

机译：分层线性建模中估计量的比较：通过最小范数二次无偏估计量来限制最大似然与自举。
6. A Targeted Maximum Likelihood Estimator of a Causal Effect on a Bounded Continuous Outcome [O] . Susan Gruber, Mark J. van der Laan -1

机译：有界连续结果因果效应的目标最大似然估计
7. A maximum smoothed likelihood estimator in the current status continuous mark model [O] . Piet Groeneboom, Geurt Jongbloed, Birgit I. Witte 2012

机译：当前状态连续标记模型中的最大平滑似然估计器

A maximum smoothed likelihood estimator in the current status continuous mark model

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