Topic: Title: An information criterion for a subset of MAR data Authors:  Keiji Takai - Kansai University (Japan) [presenting]
Kenichi Hayashi - Keio University (Japan)
Abstract: We discuss how to select a best model among candidate models with an information criterion (IC) when the data are missing at random (MAR). The problem in using the MAR data is that a subset of the MAR data may not be MAR and thus the consistent maximum likelihood (ML) estimator of interesting parameter cannot be obtained. To those data, various ICs developed so far for missing data cannot be applied because they assume that subsets of data on the candidate models are also MAR. However, this assumption is not realistic. Some of the variables that cause missingness might be excluded from the model, which result in not MAR data. Thus, we need a method to obtain the consistent ML estimator and develop an IC that can be used for subset data that are not MAR. Our goals are (i) giving a framework to obtain a consistent ML estimator for the sub-model parameter and its asymptotic distribution, (ii) developing an information criterion for the data which may not be MAR, and (iii) showing through numerical simulations how well our method works under some practical conditions.