Topics On The Estimation Of Copulas When Marginal Distributions Are Partially Unknown

Dependency analysis is a central task in multivariate analysis of statistics. Yet, the relationship between multidimensional random variables is so complex that we arc barely able to conduct a comprehensive assessment of dependent relationships between variables. Nevertheless, the fact that copula function can fully capture the relationship between variables makes it be one of the important tools for processing data dependence. Naturally, the key is how to infer unknown Copula.Firstly, this thesis briefs summarized the development history of multivari-ate dependency analysis.Some related performance indexes and the corresponding properties are introduced.In particular,as one of the most offensive tool to study the dependence Copula on overall multivariate problem, with its main properties were discussed detailed.Secondly, some importantly concepts with one involved in non-parametric stat-ical inference Copula were introduced,including empirical Copula distribution em-pirical Copula process, and its convergence rate.Finally,we considered a Copula es-timation problem with partially unknown marginal distribution.The problem is described as:Let (X1,Y1), (X2, Y2), …, (Xn, Yn) be a sequence of two-dimensional random samples from (X, Y) with independent and identically distribution. And let H(x,y), F G be the corresponding joint distribution func-tion and marginal function,respectively. Assumed that F is known,and G is un-known.Then.how to infer estimate the Copula between X and Y, and what is the convergence rate of the estimation.Based on the existing results in Copula theory, empirical distribution and em-pirical process,the above problem is explored exhaustedly. We propose a scheme to estimate the overall Copula C by sample empirical Copula C_n(u,v).The convergence of this estimate is derived with is given as follows .where 3/8???1/2.Numerical examples were also carried out to verified the obtained theoretical results.