| The comparison of population differences is a common problem in the fields of market research,economy,medicine and education.The comparison of overall differences is a part of hypothesis testing.Using the traditional parametric hypothesis test method,we need to assume that the population obeys the normal distribution,but when the type of population distribution is unknown,the traditional method is not applicable.In this paper,a semi-parametric method is mainly used to study the difference between the two population quantiles.Semi-parametric method has become one of the hotspots in the field of contemporary statistics.In recent years,a lot of research results on semi-parametric statistical analysis have been established under the semi-parametric density ratio model.The test results are often better than the traditional test methods and more effective than non-parametric methods.In this paper,a method of quantile difference is proposed to make a comparative analysis between two populations.That is to say,the hypothesis test of quantile comparison between two populations is established under the semi-parametric density ratio model.The maximum semi-parametric likelihood estimator of two population distribution functions is obtained by using the likelihood estimation method.Then the theorem of asymptotic normality of semi-parametric estimator of quantile difference between two populations is given,and estimators of the two population quantiles are obtained.And the asymptotic normality of the estimator is proved by deduction.Furthermore,we prove that semi-parametric estimators are asymptotically more efficient than non-parametric estimators.Then,through statistical simulation,it is found that this method is slightly better than the commonly used non-parameter methods when the type of the population distribution is known.When the form of the population distribution is unknown,the test semi-parametric method is works well.Finally,hypothesis testing is carried out through case analysis. |
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