Parameter expansion for estimation of reduced rank covariance matrices

Parameter expanded and standard expectation maximisation algorithms are described for reduced rank estimation of covariance matrices by restricted maximum likelihood, fitting the leading principal components only. Convergence behaviour of these algorithms is examined for several examples and contrasted to that of the average information algorithm, and implications for practical analyses are discussed. It is shown that expectation maximisation type algorithms are readily adapted to reduced rank estimation and converge reliably. However, as is well known for the full rank case, the convergence is linear and thus slow. Hence, these algorithms are most useful in combination with the quadratically convergent average information algorithm, in particular in the initial stages of an iterative solution scheme.