Variances for Maximum Penalized Likelihood Estimates Obtained via the EM Algorithm

Mark R. Segal, Department of Epidemiology & Biostatistics, University of California, San Francisco
Peter Bacchetti, Department of Epidemiology & Biostatistics, University of California, San Francisco
Nicholas P. Jewell, Division of Biostatistics, School of Public Health, University of California, Berkeley

Abstract

We address the problem of providing variances for parameter estimates obtained under a penalized likelihood formulation through use of the EM algorithm. The proposed solution represents a synthesis of two existent techniques. Firstly, we exploit the supplemented EM algorithm developed in Meng and Rubin (1991) 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 a result from Green (1990) that provides an expression for the Jacobian of the mapping induced by the EM algorithm applied to a penalized likelihood. The resultant procedure requires no additional code to that needed for the penalized EM algorithm itself.