Parameter expansion for estimation of reduced rank covariance matrices

1 ‘Parameter expanded’ and standard expectation maximisation algorithms are de2 scribed for reduced rank estimation of covariance matrices by restricted maximum 3 likelihood, fitting the leading principal components only. Convergence behaviour of 4 these algorithms is examined for several examples and contrasted to that of the aver5 age information algorithm, and implications for practical analyses are discussed. It is 6 shown that expectation maximisation type algorithms are readily adapted to reduced 7 rank estimation and converge reliably. However, as is well known for the full rank 8 case, the convergence is linear and thus slow. Hence, these algorithms are most useful 9 in combination with the quadratically convergent average information algorithm, in 10 particular in the initial stages of an iterative solution scheme. 11 restricted maximum likelihood / reduced rank estimation / algorithms / 12 expectation maximisation / average information 13