Response Missing At Random Variable Coefficients Of Statistical Inference

The varying coefficient model is an useful extention of the classical linear model. Though it has a simple formula,looked explicity,as a matter of fact it is a very common model.Many models,such as additive models,partial linear models can be viewed as special cases of it. Varying coefficient models has been developed as an new derection of the high-dimensional data regression,avoiding the so-called "cuse of dimension".It also retains the characteristics of robustness,but also has the advantage of simplifying structure and meaningful interpretation.Many scholars have been doing some researchs on it and got some good prosperities,such as Jianqing Fan of two-step estimation.Actually,however,missingness of response is very common in opinion pells,market research surveys,mail enquiries,social-economic investigations,medical studies and other scientific experiments,which caused by uncontrollable factors,falture on the part of investigator to gather correct information and so on.As a result,recently statisticians paid more attention for dealing with the problem about missing data.In order to making good use of the varying coefficient models into practice,in this paper,varying coefficient model with random missing response is investigated. To deal with missing response,complete case,imputation and inverse marginal probability wighted approaches are developled to estimated the regression coefficients respectively.All the proposed estimation for coefficients are proved to be normal asymptotic distribution.Also,we have gave the empirical log-likelihood ratio based on the inverse marginal probability weighted. We show that the proposed ratio statistic is asymptotically standard chi-square distribution under some suitable conditions and hence it canbe used to construct the confidence region for the coefficient functons.