基于半参数估计的W-CIC Copula函数选择准则

Study on weighted Copula information criterion based on semiparametric estimation

基于全参数极大似然估计的AIC准则是常用的模型选择标准.在实际应用中,往往将其用于半参数伪极大似然估计,其中存在模型选择的偏差.CIC准则适用于半参数伪极大似然估计,但对于大部分在边界处增长过快的Copula密度函数该准则失效.基于此,对原有的CIC准则进行改进建立W-CIC准则,即降低Copula密度函数在边界处的权重,是CIC准则的加权版本.W-CIC准则打破了原准则的局限性,适用于更多的Copula函数模型.

Akaike information criterion （AIC） based on fully parametric maximum likelihood estimation is a commonly used Copula function selection criterion. In practical applications, many investigations use it as a model selection criterion for the MPLE. But it exists a devia- tion in model selection. Copula Information Criterion （CIC） was developed in the semipara- metric setting. However, such a model- selection procedure cannot exist for copula models with densities that grow very fast near the edge of the unit cube. This problem affects most popular copula models. Weighted - CIC formula as a modification of CIC formula was pro- posed to down - weight the sensitivity of the pseudo - likelihood near the edge of the unit cube. It was the weighted version of CIC formula. W - CIC formula was applicable to more copula functions and breaks the limitation of CIC formula.