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Biometrika 1997 84(2):269-281; doi:10.1093/biomet/84.2.269
© 1997 by Biometrika Trust
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On the rate of convergence of the ECME algorithm for multiple regression models with t-distributed errors

JEANNE KOWALSKI, XIN M. TU, ROGER S. DAY and JOSÉ MENDOZA-BLANCO

Department of Mathematics and Statistics, University of Pittsburgh Pittsburgh, Pennsylvania 15260, U.S.A. e-mail: JJK+{at}pitt.edu xintu+{at}pitt.edu
Department of Biostatistics, University of Pittsburgh Pittsburgh, Pennsylvania 15260, U.S.A. e-mail: day{at}zydeco.pci.upmc.edu
Universidad Nacional Autónoma de México, Facultad de Ciencias, Departamento de Matemáticas Circuito Exterior, Cd. Universitaria. c.p. 04510, México, D.F., México e-mail: jmendoza{at}escher.fciencias.unam.mx

Although much work has been done on comparing and contrasting the EM and ECME algorithms, in terms of their rates of convergence, it is not clear what mechanism underlies each and, furthermore, what factors may determine and influence their rates of convergence. In this paper, we examine the convergence rates and properties of these two popular optimisation algorithms as used in computing the maximum likelihood estimates from regression models with t-distributed errors. By approaching this computing problem through the use of two data augmentation schemes, as well as variations of these well-known algorithms, we offer a more composite view on the performance of each.

Key Words: ECME • EM • Maximum likelihood • Step-length Newton's method • t-distribution


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