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SUMMARY We address the problem of providing variances for parameter estimates obtained under a penalized likelihood formulation through use of the EM algorithm. The solution proposed represents a synthesis of two existent techniques. Firstly, we exploit the supplemented EM algorithm developed by Meng and Rubin that provides variance estimates for maximum likelihood estimates obtained via the EM algorithm. Their procedure relies on evaluating the Jacobian of the mapping induced by the EM algorithm. Secondly, we utilize results from Green that provide expressions for Jacobians of mappings induced by EM algorithms applied to a penalized likelihood. The resultant procedure requires no more code than that needed for the penalized EM algorithm itself. The technique is demonstrated with an illustrative example.
Segal et al. (Fri,) studied this question.