Fitting Copulas with Maximal Entropy - Milan Bubák; Mirko Navara (Entropy)
We deal with two-dimensional copulas from the perspective of their differential entropy. We formulate a problem of finding a copula with maximum differential entropy when some copula values are given. As expected, the solution is a copula with a piecewise constant density (a checkerboard copula). This allows us to simplify the optimization of the continuous objective function, the differential entropy, to an optimization of finitely many density values. We present several ideas to simplify this problem. It has a feasible numerical solution. We also present several instances that admit closed-form solutions.