A Simple Method for Obtaining the Information Matrix for a Multivariate Normal Distribution
William B. Smith, Ronald Raymond Hocking · The American Statistician · 1968
The purpose of this note is to present a simple method for finding the informnation matrix, and its inverse, for the p-variate normal distribution, N(O,2). Corresponding matrices for N(,u,) are easily obtained since they are block diagonal and the portion corresponding to , presents no difficulty. The simplicity of the technique presented here arises froin the fact that both the information matrix and its inverse can be expressed as the product of a diagonal matrix with a matrix whose elements are given by a simple set of formulas. The basic technique is extended to the case in which some observations on one of the variates are missing, and is illustrated by an example.