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Biometrika 2000 87(3):651-662; doi:10.1093/biomet/87.3.651
© 2000 by Biometrika Trust
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ECM algorithms that converge at the rate of EM

J Sexton and AR SwensenZ

Statistics Norway, N-0033 Oslo, Norway E-mail: jse@ssb.no Z Department of Mathematics, University of Oslo, N-0316 Oslo, Norway E-mail: swensen@math.uio.no

We show that the ECM algorithm can always be constructed to converge at the same or approximately the same rate as the EM algorithm. The construction is based on the well-known conjugate directions algorithm. This result both suggests ways of speeding up the convergence of ECM and provides a simple way of identifying cases where the simplicity and stability of ECM over EM is attained at effectively no loss in convergence speed. Three examples are given.

Key Words: conjugate directions algorithm; ECM algorithm; EM algorithm; missing data; orthogonal parameters; rate of convergence


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