ROBUST PREDICTIVE DISTRIBUTIONS BASED ON THE PE- NALIZED BLENDED WEIGHT HELLINGER DISTANCE By CHANSEOK PARK, IAN R. HARRIS and AYANENDRANATH BASU Department of Statistics, Pennsylvania State University, University Park, PA 16802, USA Department of Mathematics, Northern Arizona University, Flagstaff, AZ 86011, USA Indian Statistical Institute, Computer Science Unit, Calcutta 700 035, INDIA Key words and phrases: Hellinger distance; prediction; penalty functions; effi- ciency. ABSTRACT Harris (Biometrika, 1989) suggests a predictive distribution based on boot- strapping using the maximum likelihood estimator of an unknown parameter. Basu and Harris (Biometrika, 1994) introduce robust estimative and bootstrap predictive distributions for discrete models by using the minimum Hellinger distance estimator of the unknown parameter instead of the maximum likeli- hood estimator. Generalizing the results of Basu and Harris, the present pa- per considers parametric predictive distributions using the minimum penalized blended weight Hellinger distance estimator for discrete models. Monte Carlo simulations suggest that the proposed predictive distributions are attractive robust substitutes for the usual predictive distributions based on the maxi- mum likelihood estimator under data contamination, and perform favorably compared to the predictive distributions suggested by Basu and Harris. 1. INTRODUCTION The maximum likelihood estimator, which is often optimal under the as- sumed model, may be quite sensitive to small deviations from model assump- tions. Several authors (Beran 1977, Simpson 1987, Lindsay 1994) have studied 1