Convergence of the Monte Carlo Em for Curved Exponential Families
نویسنده
چکیده
SUMMARY The Monte Carlo Expectation Maximization (MCEM) algorithm (Wei and Tanner (1991)), a stochas-tic version of EM, is a versatile tool for inference in incomplete data models, especially when used in combination with MCMC simulation methods. Examples of applications include, among many others: regression with missing values (Wei and Tanner (1991)), time-series analysis (Chan and Ledolter (1995)), hierarchical generalized linear models (Booth and Hobert (1999)). In this contribution, the convergence of MCEM is established under conditions on the imputation techniques weaker than those stated by Chan and Ledolter (1995). It is shown, using uniform version of ergodicity theorems for Markov chains, that MCEM converges under weak conditions on the simulation kernel, veriied, e.g. by the random walk Hastings-Metropolis algorithm and the independent sampler. The rate of convergence is studied, showing the impact of the simulation schedule on the uctuation of the parameter estimate at the convergence. A novel averaging procedure is then proposed to reduce the simulation variance.
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