响应变量存在缺失时非线性半参数回归模型的经验似然推断

在许多实际问题的研究中,例如临床试验、民意测验、社会问卷调查等,经常导致数据的缺失,而通常使用的统计方法都需要在样本数据完整的情况下进行.如何处理样本中的缺失数据,使得统计推断得以顺利进行,近年来越来越引起人们的广泛关注.针对响应变量存在缺失时的非线性半参数回归模型Y=f（X,β）＋g（T）＋ε,研究了参数β的经验似然推断.在一定条件下,分别基于一般借补数据和修正借补数据的情形,得到了关于参数β的对数经验似然统计量渐近服从χ2分布,并由此可以构造出关于参数β的置信域.

Empirical likelihood for nonlinear semi-parametric regression model with missing response data

In the study of many practical problems,such as the clinical trials;poll;community questionnaire,various reasons could very easily lead to a large number of data missing and most of the statistical methods are required a complete data of a sample.So in recent years people concern more and more about how to handle missing data,making statistical inference process going smoothly.This article studies the empirical likelihood of β in the nonlinear semi-parametric regression model Y=f（X,β）＋g（T）＋ε with missing response data.Under certain conditions,based on the general imputation data and corrected imputation data,investigates the empirical likelihood of β.The conclusion is the empirical log-likelihood statistics of β is asymptotically distributed as a chi-square. Based on this,the confidence region of β can then be constructed.