Clustering Data with Nonignorable Missingness using Semi-Parametric Mixture Models
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We are concerned in clustering continuous data sets subject to nonignorable missingness. We perform clustering with a specific semi-parametric mixture, avoiding the component distributions and the missingness process to be specified, under the assumption of conditional independence given the component. Estimation is performed by maximizing an extension of smoothed likelihood allowing missingness. This optimization is achieved by a Majorization-Minorization algorithm. We illustrate the relevance of our approach by numerical experiments. Under mild assumptions, we show the identifiability of our model, the monotony of the MM algorithm as well as the consistency of the estimator. We propose an extension of the new method to the case of mixed-type data that we illustrate on a real data set.
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