区间删失数据下部分线性模型的经验似然统计推断

Empirical Likelihood Statistical Inference for Partial Linear Models Under Interval Censored Data

文章将部分线性模型的经验似然推广到Ⅰ型区间删失数据上。受许多因素的影响,数据往往不具有完整性,因此Ⅰ型区间删失数据在医疗领域中十分常见,对该数据的研究有十分重要的意义。由于Ⅰ型区间删失数据不能精准观测到事件发生时间的特殊性,无法直接用该数据对部分线性模型进行研究,因此使用无偏转换方法对数据进行处理,然后使用核估计、经验似然等方法对参数进行估计,并详细证明经验似然方程的相合性和渐近正态性。通过模拟研究,可以看出不同模型下的参数覆盖率随着样本量的增大越来越接近置信水平,模拟结果良好。从QQ图可以看出经验似然统计量渐近服从卡方分布。实证分析了RFM小鼠医疗数据,分析结果证明了该方法的实用性。

This paper extends the empirical likelihood of partial linear models to CaseⅠinterval censored data.Affected by many factors,the data is often incomplete,so CaseⅠinterval censored data is very common in the medical field,and the research on the data is of great significance.The particularity that CaseⅠinterval censored data cannot accurately observe the occurrence time of events makes it impossible to directly use the data to study partial linear models.Therefore,the paper employs the unbiased transformation method to process the data,and then uses the kernel estimation,empirical likelihood and other methods to estimate the parameters.Finally,the paper demonstrates in detail the consistency and asymptotic normality of the empirical likelihood equation.Through the simulation research,it can be seen that the parameter coverage under different models is closer to the confidence level as the sample size becomes larger,and that the simulation results are good.The QQ graph shows that the empirical likelihood statistics asymptotically obey a chi-square distribution.The paper also empirically analyzes RFM mouse medical data,and the results prove the practicability of this method.