Consistency of information criteria for model selection with missing data

ABSTRACT

In this paper, we investigate the consistency of the Expectation Maximization (EM) algorithm-based information criteria for model selection with missing data. The criteria correspond to a penalization of the conditional expectation of the complete data log-likelihood given the observed data and with respect to the missing data conditional density. We present asymptotic properties related to maximum likelihood estimation in the presence of incomplete data and we provide sufficient conditions for the consistency of model selection by minimizing the information criteria. Their finite sample performance is illustrated through simulation and real data studies.     

Resampling for Order Estimation of Autoregressive Models with Missing Data

In this article, we consider the order estimation of autoregressive models with incomplete data using the expectation–maximization (EM) algorithm-based information criteria. The criteria take the form of a penalization of the conditional expectation of the log-likelihood. The evaluation of the penalization term generally involves numerical differentiation and matrix inversion. We introduce a simplification of the penalization term for autoregressive model selection and we propose a penalty factor based on a resampling procedure in the criteria formula. The simulation results show the improvements yielded by the proposed method when compared with the classical information criteria for model selection with incomplete data.