Empirical Likelihood Estimator Of The Accelerated Failure Time Model With Missing Covariates

In clinical trials and other practical applications,due to human or some objective reasons,data often are missing.If there is no suitable statistical method,there may be some deviations in the results,which will lead to statistical inference errors.In recent years,the study of missing data has been discussed in detail by statisticians and scholars,but there are few studies on such problems under the accelerated failure time model.The accelerated failure time model is a semiparametric model with strong practicality and research value in the survival analysis.Therefore,the main topic of this study is to enrich the previous research results.Empirical likelihood is an effective nonparametric statistical inference method.It has many outstanding advantages in constructing point estimatior and confidence interval estimator about parameters concerned and is applied to many fields by many researchers.In this paper,we mainly consider the accelerated failure time model under the condition that partial covariates are randomly missing.We have discussed the following two aspects:1)the IPW estimation is proposed.If the missing probability is a nonparametric model,we use kernel estimation estimate missing probability,but if the dimensionality is too high,the nonparameter estimation will encounter "dimension disaster",then we make the missing probability as the parameter model to discuss and use the inverse probability weighting method to construct the estimation equation.We use the method of transformation to the optimization problem to get the solution of the estimation equation,and the asymptotic distribution of the estimate.2)the ELW estimation is proposed.If the missing probability is large enough,the inverse probability weighting method cannot be completely using the effective information hidden in incomplete data,we will lose part of estimation efficiency.So we use the idea of empirical likelihood weighting to build new weights to improve the estimation efficiency and prove the asymptotic normality of the ELW estimator.Comparing the asymptotic variance,we can see that ELW estimation is more effective than IPW estimation.By comparing the deviation and the root mean square error by numerical simulation,it shows that the performance of ELW estimator is better than that of IPW and CCA estimation.In this paper,we discuss the empirical likelihood inference of accelerated failure timemodel with covariate missing,the framework is as follows:In the first chapter,we analyze the research situation of accelerated failure time model,and introduce the development of missing data and empirical likelihood method.In the second chapter,under the accelerated failure time model with covariates missing,we first introduce the CCA estimation of the regression parameters and put forward the inverse probability weighting(IPW)estimation and gives the asymptotic distribution of the IPW estimation.Then,we also put forward the empirical likelihood weighting(ELW)estimation and the asymptotic normality of the ELW estimation.Finally,we introduce the MM algorithm used in the solution.In the third chapter,numerical simulation compares the estimation mentioned above from the perspective of deviation and root mean square error.