Statistical inference for nonignorable missing-data problems: a selective review

Nonignorable missing data are frequently encountered in various settings, such as economics, sociology and biomedicine. We review statistical inference for nonignorable missing-data problems, including estimation, influence analysis and model selection. For estimation of mean functionals, we review semiparametric method and empirical likelihood (EL) approach. For estimation of parameters in exponential family nonlinear structural equation models, we introduce expectation-maximisation algorithm, Bayesian approach, and Bayesian EL method. For influence analysis, we investigate the case-deletion method and local influence analysis method from the frequentist and Bayesian viewpoints. For model selection, we present the modified Akaike information criterion and penalised method.