Bernstein Estimation Of Joint Distributions Based On Copula Method

The rapid development of international financial globalization has strengthened the interdependence of markets.Multivariate analysis emphasizes the correlation analysis among variables.The analysis of price to return and the measurement of risk are closely related to the study of the correlation between variables.The introduction of Copula provides a new method to study these multidimensional joint distributions.In this method,the joint distribution is decomposed into a Copula function and several edge distribution functions,which greatly simplifies the difficulty of analysis.In the study of specific problems,the estimation of Copula function occupies an important position.This paper studies the estimation of the Copula function and the joint distribution function.First,the current research status of the Copula method is introduced;secondly,the Bernstein estimation of the Copula function and the joint distribution function is given,and a proof of the consistency of the estimates is given;Finally,a numerical study demonstrates the effectiveness of the method.