A hybrid approach for regression analysis with block missing data

Missing data often arise in practice. The commonly employed approach to handle the missing data is imputation, which is effective when the missing mechanism is known and each subject in the data set misses at random. However, the situation where the imputation is not appropriate often emerged. Because in that situation, some data are not missing at random, so a hybrid estimate, where the Bayesian and frequentist approaches are used for inferring the parameters with and without prior information respectively, is proposed. The asymptotic properties of the hybrid estimator are also provided. Numerical results including simulation studies and data analysis about grade point average (GPA) are conducted to show the performances of the proposed method.