Estimating Copula Density Using Minimum Information Method based on the First and Second Kind of Chebyshev Polynomials:Comparison Study

Estimating Copula Density Using Minimum Information Method based on the First and Second Kind of Chebyshev Polynomials:Comparison Study

In the present paper, we try to estimate copula density using minimum information ap- proaches through the first and second kind of orthogonal Chebyshev polynomials as a basis function. The basic idea behind this method is to use a two-dimensional Chebyshev poly- nomial series to approximate any log-density of a bivariate copula function by truncating the series at an appropriate point. In addition, a comparison study implemented between first and second kind of orthogonal Chebyshev polynomials. The finding results show the superiority of first kind of orthogonal Chebyshev polynomials in application.