Inference For The Difference Of Bonferroni Indexes Based On Jackknife Empirical Likelihood Method And Its Application

With the development of society and economy,the gap between the rich and the poor is a common problem which should be concerned continually.On the measurement of the gap between the rich and the poor,many researchers defined di?erent economic indicators,including Gini coe cient,Bonferroni index,and so on.At present,Gini coe cient is widely used in academia and practical application,while researchers pay less attention to Bonferroni index.However,compared with Gini coe cient,Bonferroni index gives the low-income groups more weight in the construction of expression.Therefore,Bonferroni index is more sensitive to the low-income groups in measuring the gap between the rich and the poor.Noting the advantages of Bonferroni index,in recent years,many researchers draw attention on the problem of statistical inference about Bonferroni index and we will continue to explore this problem.By comparing two di?erent income distributions of Bonferroni index,we will study the gap between rich and poor in two countries or regions at the same time or in the same country or region at di?erent time.In this thesis,we make statistical inference to the di?erence of two Bonferroni indexes and we propose jackknife empirical likelihood method to construct the statistic of the di?erence of two Bonferroni indexes.Furthermore,under certain conditions,we prove that the proposed jackknife empirical likelihood ratio asymptotically converges to the standard chi-squared distribution with the degree of freedom one.Then,we can construct the confidence interval of the di?erence of two Bonferroni indexes.Meanwhile,the method proposed in this paper is compared with the standard asymptotic normal method and Bootstrap method.Through a large number of numerical simulations and a set of examples of British household expenditure data,the feasibility and superiority of the method proposed in this paper are demonstrated by comparing the coverage rate and confidence interval length.