A Study On Hypothesis Testing Method Of The Difference Of Two Population Means Under A Semiparametric Density Ratio Model

Testing on the difference of two population means is an important element of hypothesis testing. In tradition the testing on the difference of two population means is often under the normal distribution assumption. But when the distribution is not normal, the test is not obvious and even failure. In this paper, a new method is proposed for testing on the difference of two population means. For the difference of two population means testing, we put forward a semiparametric hypothesis testing method which is under a semiparametric density ratio mode. This method is essentially built upon semiparametric estimation of the difference of two population means. Some theoretical results as well as simulation results are provided, also presented are the analysis of real data sets. The simulations suggest that our proposed method is slightly superior to some commonly used parametric and nonparametric methods when data are normal,and is significantly better than them when data are not normal. The analysis of real data sets show that our proposed method for testing on the difference of two population means is same with the t test when the population is normal, and is same with the nonparametric method when the population's distribution is unknown.In chapter 1, the significance of the difference of two population means is introduced, and the assumption is a semiparametric density ratio model. Secondly, we review the history of semiparametric density ratio model and how to test the validity of the model. At last resent studies on the semiparametric density ratio model are described.In chapter 2, under the semiparametric density ratio model, we give the semiparametric estimation of the difference of two population means.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 the proposed semiparametric method.In chapter 5, real examples are analysed by the method we proposed.At last, we make a summary of the paper and give a prospect.