Robust predictive distributions for exponential families

The bootstrap predictive distribution considered by Harris (1989) is modified by replacing the maximum likelihood estimator of the unknown parameter by its minimum Hellinger distance estimator. The predictive distribution thus obtained is asymptotically superior to the corresponding estimative distribution in terms of the average Kullback-Leibler divergence, when the true distribution is in the natural exponential family. Simulation results are provided for the binomial and normal distributions which suggest that the proposed predictive distributions are robust and can perform better than the likelihood based methods under data contamination.