Initialization for NORTA: Generation of Random Vectors with Specified Marginals and Correlations

Abstract

We propose a specific method for generating n-dimensional random vectors with given marginal distributions and correlation matrix. The method uses the NORTA (NORmal To Anything) approach, which generates a standard normal random vector and then transforms it into a random vector with specified marginal distributions. During initialization, n(n-1)/2 nonlinear equations need to be solved to ensure that the generated random vector has the specified correlation structure. To solve these equations, we apply retrospective approximation, a generic stochastic root-finding algorithm, with slight changes. Internal control variates are used to estimate function values. Empirical comparisons show that the control-variate variance-reduction technique improves the algorithm's convergence speed as well as its robustness. Simulation results for a variety of marginal distributions and correlation matrices are also presented.