Asymptotic Approximations Of Random Ratio Model Based On AANA Sequences

The inverse moment’s research can be used in many fields such as risk evaluation and insurance mathematics.In this paper,we consider the weighted inverse moment model based on asymptotically almost negatively associated(AANA,in short)sequences.Under some weak condition,we obtain the asymptotic approximation of inverse moments and its convergence rate.As applications of inverse moments,we study the random ratio models which contain the change-point detection models,and obtain the asymptotic moment approximation of random ratio and its convergence rate.Our conditions of inverse moment and random ratio models are very weaker than the existing models.In order to test our results,we do some simulations and real data analysis in this paper.Our results improve and general the existing works.In Chapter 1,we introduce the background knowledge,research methods and research status of inverse moment.At the same time,some important definitions and lemmas are given,including the definition of AANA sequence,the properties of A AN A and the equivalent conditions of inverse moment under suitable conditions.In Chapter 2,we study the asymptotic approximation and convergence rate of inverse moment under the condition of finite first moment.First,we prove the equivalence relation of inverse moment under the given conditions.That is E(a+Xn)-α～(a+EXn)-α,(?)α>0.Then,the convergence rate of inverse moment is obtained by using Taylor formula,AANA’s moment inequality and Holder inequality.Finally,under the different weighted sequences,considering the homoscedasticity case and heteroscedasticity case,we study the finite sample performance of the ratio models E(a+Xn)-α/(A+EXn)-α and test the equivalence relation of inverse moments.In Chapter 3,we study the asymptotic approximation and convergence rate of random ratio model.In Chapter 2,we study the asymptotic approximation of the inverse moment and the rate of convergence.On this basis,we consider the random ratio model.As an application of the model E[Xn/(a+Yn)],we remove the parameter a and study the model E(Xn/Yn).By using Taylor formula and moment inequality,the asymptotic approximation and convergence rate of stochastic ratio model are obtained,which weakens the condition in Yang et al.[1].In Chapter 4,we carried out real data analysis of inverse moment and random ratio models.For example,we construct a variance change point model based on the height data of male and female students in the university.We test the function of the model Xn/Yn in the variance change point model when the variance change point is known.Meanwhile,we give the variance change point models for the changes of return of IBM stock price.With the help of variance change point estimators and Xn/Yn,we find the same change-point locations.In addition,some economic reasons are illustrated for these change point locations.In Chapter 5,we summarize our works in this thesis and give some discussion for the future research of variance change point models.