Empirical Likelihood For Nonlinear Semi-parametric Regression Model With Missing Response Data

In the study of many practical problems, such as the clinical trials in the tracking of a newly developed drug in medical research; 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 that statistical inference trapped into difficulties. So in recent years people concern more and more about how to handle missing data, making statistical inference process going smoothly. When there is missing data, it is easy to think to complete the missing data firstly, in order to get full data sample and then applied the usual statistical methods to infer.The first chapter recommends the empirical likelihood theorem,and emphasizes on the missing mechanism and its methods of missing data.The second chapter introduces nonlinear semi-parametric regression model Y = f ( X ,β) + g (T )+ε.Based on the complete-case data and imputed data of the sample individually, investigates the empirical likelihood ofβ. Need to point out is that the imputation is further divided by the imputed values and corrected data when considering imputation data. The conclusion of that is the asymptotic normality ofβand its empirical log-likelihood ratio function is asymptotically distributed as a chi-square. Then, by using the bias-correction technique and weighted semi-parametric regression imputation, we obtain a weight-corrected empirical log-likelihood ratio function forθis asymptotically distributed as a chi-square with one degree of freedom and the asymptotic normality of (?)The third chapter conducts one-dimensional numerical simulation under the sample data.The fourth chapter puts forward five lemmas and their proofs, and also proves the main conclusions of that the second chapter got.