CC15-2006: Generating Multivariate Normal Data by Using PROC IML

In simulation studies in statistics, there are many situations that we need to generate data from a multivariate normal distribution. By multivariate normal data we mean joint observations of p variables Y1, Y2, . . . , Yp, in which each individual variable by itself is normally distributed, the variables are mutually correlated, and come from a joint multivariate normal distribution. The procedure for generation of multivariate normal data is similar to the univariate case, that is, we can generate pairs of independent normals and then multiplied that pairs by the Cholesky square root of the desired variancecovariance matrix. One way to do that is to obtain the formula for the Cholesky square root of the variance-covariance matrix, and which is easy for bivariate normal data. However, it becomes complicated when p is large. An alternative method by using PROC IML can be used to accomplish the desired data easily by using matrix computations. Function HALF in PROC IML can be used to obtain the Cholesky square root of the desired variance-covariance matrix.