ML-ESTIMATION OF THE T-DISTRIBUTION USING EM AND ITS EXTENSIONS, ECM AND ECME

The multivariate t distribution has many potential applications in applied statistics. Current computational advances will make it routinely available in practice in the near future. Here we focus on maximum likelihood estimation of the parameters of the multivariate t, with known and unknown degrees of freedom, with and without missing data, and with and without covariates. We describe EM; ECM and ECME algorithms and indicate their relative computational efficiencies. All three algorithms are analytically quite simple, and all have stable monotone convergence to a local maximum likelihood estimate. ECME, however, can have a dramatically faster rate of convergence.