Statistica Sinica

David A. van Dyk, Xiao-Li Meng and Donald B. Rubin***

Abstract:This paper provides detailed theory, algorithms, and illustrations for computing asymptotic variance-covariance matrices for maximum likelihood estimates using the ECM algorithm (Meng and Rubin (1993)). This Supplemented ECM (SECM) algorithm is developed as an extension of the Supplemented EM (SEM) algorithm (Meng - Rubin (1991a)). Explicit examples are given, including one that demonstrates SECM, like SEM, has a powerful internal error detecting system for the implementation of the parent ECM or of SECM itself.

Key words and phrases:Contingency table, convergence rate, EM algorithm, Fisher information, incomplete data, IPF, missing data, SEM algorithm.