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Empirical likelihood method for non-ignorable missing data problems

机译:不可忽略的缺失数据问题的经验似然法

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摘要

Missing response problem is ubiquitous in survey sampling, medical, social science and epidemiology studies. It is well known that non-ignorable missing is the most difficult missing data problem where the missing of a response depends on its own value. In statistical literature, unlike the ignorable missing data problem, not many papers on non-ignorable missing data are available except for the full parametric model based approach. In this paper we study a semiparametric model for non-ignorable missing data in which the missing probability is known up to some parameters, but the underlying distributions are not specified. By employing Owen (1988)'s empirical likelihood method we can obtain the constrained maximum empirical likelihood estimators of the parameters in the missing probability and the mean response which are shown to be asymptotically normal. Moreover the likelihood ratio statistic can be used to test whether the missing of the responses is non-ignorable or completely at random. The theoretical results are confirmed by a simulation study. As an illustration, the analysis of a real AIDS trial data shows that the missing of CD4 counts around two years are non-ignorable and the sample mean based on observed data only is biased.
机译:在调查抽样,医学,社会科学和流行病学研究中,普遍缺少响应问题。众所周知,不可忽略的丢失是最困难的丢失数据问题,其中响应的丢失取决于其自身的价值。在统计文献中,与可忽略的缺失数据问题不同,除了基于完全参数模型的方法外,关于不可忽略的缺失数据的论文很少。在本文中,我们研究了不可忽略的缺失数据的半参数模型,该模型的缺失概率在某些参数下是已知的,但是未指定基础分布。通过使用Owen(1988)的经验似然方法,我们可以得到失概率和均值响应中参数的约束最大经验似然估计值,这些估计值被证明是渐近正态的。此外,似然比统计量可用于测试响应缺失是不可忽略的还是完全随机的。理论结果通过仿真研究得到证实。例如,对真实的AIDS试验数据的分析表明,两年左右CD4计数的缺失是不可忽略的,并且仅基于观察到的数据的样本均值是有偏差的。

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