On Effectiveness of Decomposition Methods to Generate Multivariate Normal Variates: A Comparative Study

Abstract

The multivariate normal density (MVN) is considered to be the underlying distribution of many observed samples in statistics for modelling purpose. Therefore, simulating sample from the MVN is required to verify the efficiency of the fitted model. Decomposition based approach is currently being used to simulate sample from MVN whose building block is Cholesky or eigen decomposition. Unfortunately, there is no concrete study in the literature so far regarding the efficient decomposition technique between these two1. In this paper, an attempt is made to determine the efficient decomposition technique between these two in the context of MVN generation through an extensive simulation study. From our simulation study, it is observed that in general the Cholesky decomposition is numerically faster than the eigen decomposition.