带缺失数据的半参数非线性模型基于经验似然的统计诊断

Diagnostic and empirical likelihood for semi-parametric nonlinear model with missing data

研究了用经验似然的方法来研究带有缺失数据的半参数非线性模型的统计诊断问题。首先,在响应变量完全随机缺失下,利用修正借补的方法处理缺失数据,从而得到完全样本;然后用核估计方法对未知函数进行估计。其次,基于数据删除模型给出了参数的一步近似估计,提出了经验Cook距离以及标准化残差分析,进而找出异常点和强影响点。最后,通过实例对带有缺失数据的非线性半参数模型进行统计分析来验证以上方法的可行性和有效性。

Present a unified diagnostic method based on empirical likelihood for the semi-parametric nonlinear regression models with missing data. First,assume that the responses are missing completely at random; impute missing data and get complete sample. Then,through kernel estimation to estimate the unknown function,and the parameter estimate equation based on the experience of application of likelihood methods to estimate. Experience based on the deletion model proposed experience like natural cook distance,and standardized residuals,then find outliers and strong impact point. Finally,a real data is given to illustrate the validity of statistical diagnostic measures.