Copula Information Criterion Based On Semiparametric Estimation

The model is used to reflect and describe how people understand the objective phenomenon.Using the collected data to establish the corresponding model has become an important study approach to research some related problems. Among them,model selection problems as the basis of statistical analysis, are of great research significance.Copula is the function which connects the marginal distribution with the joint distribution function.As an effective data modeling tool,Copula is widely used in various areas.The primary task that using Copula to establish model is to choose a suitable one from the given Copulae families.Akaike information criteri-on(AIC) based on fully parametric maximum likelihood estimation is a commonly used Copulae function selection criterion.In practical applications,many investi-gations use it as a model selection criterion for the MPLE. But it exists a de-viation in model selection.Copula Information Criterion(CIC) was developed in the semiparametric setting. However, such a model-selection procedure cannot exist for copula models with densities that grow very fast near the edge of the u-nit cube.This problem affects most popular copula models.In order to research on above-mentioned problems,this text establishes Copula function selection criterion for semiparametric estimation and gives related analysis.Firstly,it introduces the related knowledge of Copula, includes the commonly used copulae and the estima-tion of parameters.Then,it elaborates several important Copula function selection criterion,includes AIC,CIC and xv-CIC,expatiated the scope of application of each model selection criterion and developing process.Developing Weighted Copula In-formation Criterion,as a modification of CIC formula,is proposed to down-weight the sensitivity of the pseudo-likelihood near the edge of the unit cube.It is the weighted version of CIC formula.w-CIC formula is applicable to more copulae functions and breaks the limitation of CIC formula.At last,the text applies monte carlo simulation method to compare AIC with CIC systematically and proposes the issues for the further research.