An iterative copula method for probability density estimation

We propose a method for reconstructing a probability density function (pdf) from a sample of an n-dimensional probability distribution. The method works by iteratively applying some simple transformations until the sample becomes close enough to normal. Then we construct the desired pdf by applying the same transformations to the normal pdf in the backward order. We illustrate this method with two examples. For the first example the sample is drawn from a distribution that is known in advance, and for the second example we run the method on a sample of normalized equity returns. We also provide a theoretical justification of the method by proving that the same transformations applied to the original probability distribution will make it weakly converge to the n-dimensional normal distribution.;