| Case-control study is often adopted in the field of medical diagnosis research.When we need to compare two different medical diagnosis methods,from the same experiment object we will get test data of two diagnosis methods,and it will generate binary case control data.The traditional test on the mean difference is based on the the normal distribution assumption,and when the overall distribution is not Gaussian,the effect is not obvious or even failure.In this paper,we put forward the hypothesis test of two population mean difference under a semiparametric density ratio model.This method is mainly based on the semiparametric estimation of the difference of two means.Statistical simulation shows that this method is slightly better than the usual parametric and non parametric methods when the data is in line with the normality assumption.It is very obviously better when the data is not normal.The first chapter is introduction,we firstly introduce the significance of testing on the difference of two population means under a semiparametric density ratio model.Secondly,we review the history of semiparametric density ratio models and how to test the validity of the model.At last recent studies on the semiparametric density ratio model are described.In chapter 2,we give the semiparametric estimation of the difference of two population means under a bivariate semiparametric density ratio model.In chapter 3,we derive the asympotic distributions of the newly proposed estimators and show that they are more efficient than traditional nonparametric methods.At last,the Wald semiparametric test statistic is constructed.In chapter 4,a simulation study is presented to give the achieved significance levels and powers of a parametric t test method,a nonparametric method and our semiparametric method.In chapter 5,we apply our proposed method to anlysis of real examples.The sixth chapter is a summary of this thesis and comments on the prospect study for the future research. |
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