## Monte Carlo likelihood inference for missing data models.(English)Zbl 1124.62009

Summary: We describe a Monte Carlo method to approximate the maximum likelihood estimate (MLE), when there are missing data and the observed data likelihood is not available in closed form. This method uses simulated missing data that are independent and identically distributed and independent of the observed data. Our Monte Carlo approximation to the MLE is a consistent and asymptotically normal estimate of the minimizer $$\theta^*$$ of the Kullback-Leibler information, as both Monte Carlo and observed data sample sizes go to infinity simultaneously. Plug-in estimates of the asymptotic variance are provided for constructing confidence regions for $$\theta^*$$. We give logit-normal generalized linear mixed model examples, calculated using an $$R$$ package.

### MSC:

 62F12 Asymptotic properties of parametric estimators 65C05 Monte Carlo methods 62J12 Generalized linear models (logistic models)

bernor; R
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