A method to generate multivariate data with moments arbitrary close to the desired moments

We show how it is possible to generate multivariate data which have moments arbitrary close to the desired ones. They are generated as linear combinations of variables with known theoretical moments. It is shown how to derive the weights of the linear combinations in both the univariate and the multivariate setting. The use in bootstrapping is discussed and examplified with an Monte Carlo simulation where the importance of the ability of generating data with control of higher moments is shown.