Generation of random matrices with orthonormal columns and multivariate normal wariates with given sample mean and covariance

Abstract

In this paper, an algorithm for generating random matrices with orthonormal columns is introduced. As pointed out by a referee, the algorithm is almost identical to Wedderburn's (1975) unpublished method. The method can also be considered as an extension of Stewart's (1980) method, which was designed to generate random orthogonal matrices. It is found outperforming a simple extension of the QR factorization method and that of Heiberger's (1978) method. This paper also demonstrates how the algorithm can be used in generating multivariate normal variates with given sample mean and sample covariance matrix.

Keywords:

• Monte Carlo simulation
• multivariate normal simulation
• random orthogonal matrices