Probit and Improved Probit Transform-Based Kernel Estimator for Copula Density

Abstract

Copula modeling is widely used in modern statistics. The boundary bias problem is one of the problems faced when estimating by nonparametric methods, as kernel estimators are the most common in nonparametric estimation. In this paper, the copula density function was estimated using the probit transformation nonparametric method to eliminate the boundary bias problem that suffers kernel estimators. Simulation was also employed for three nonparametric methods to estimate the copula density function and we proposed a new method that is better than the rest of the methods by five types of copulas with different sample sizes and different levels of correlation between the copula variables and the different parameters for the function. The results showed that the best method is to combine probit transformation and mirror reflection kernel estimator (PTMRKE) and followed by the (IPE) method when using all copula functions and for all sample sizes. If the correlation is strong (positive or negative). However, in the case of using weak and medium correlations, it turns out that the (IPE) method is the best, followed by the proposed method (PTMRKE), depending on (RMSE, LOGL, Akaike) criteria. The results also indicated a weak mirror kernel reflection method when using the five copulas.

Paper type: Research paper.