The Use of Non-Parametric Methods to Estimate Density Functions of Copulas


Munaf Yousif Hmood,Zainab Falih Hamza,



Copula functions,Transformation kernel,Beta kernel,LocalLikelihood transformation Estimator,


Copulas distinguish the dependence among random vectors components as opposed to marginal and joint distributions, which can be directly observed, thus,so the copulas are considered as a hidden dependence among random vectors. Hence , the copulas could be defined as a structure that connects the joint distribution with the marginal distribution based on the non-parametric estimation with the use of the kernel function by the existence of the copula as it is considered as a tool hugely used in the modern statistics and more used in the non-parametric estimations; besides indicating the general characteristics of the estimator and selecting the appropriate bandwidth through the simulation process. A comparison was carried out between transformation estimator and Beta estimator and local likelihood transformation(LLTE) estimator in the estimation of the probability density function , using bimodel normal distribution. The results of simulation showed , according to the measurement of comparison used , that the best method is the method of (LLTE), where V. good estimations and easily to be implemented have been obtained while reducing boundary effect problems.


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