ROBUSTIFICATION OF THE MLE WITHOUT LOSS OF EFFICIENCY

Biman Chakraborty, Ayanendranath Basu and Sahadeb Sarkar

The minimum Hellinger distance estimator (MHDE) is known to be both robust under data contamination and asymptotically efficient at the model. Lindsay (1994) introduced a family of density based divergences, called disparities, containing the Hellinger distance and many other well known divergences. He also introduced the concept of the residual adjustment function (RAF) of the disparity that plays a crucial role in determining the efficiency and robustness properties of the corresponding minimum disparity estimators. In this paper we examine a modified version of the RAF of the likelihood disparity (LD), which is linked to the maximum likelihood estimator (MLE). This modified RAF resembles Huber's (1964) ψ function in M-estimation. The corresponding estimators are naturally robust and second order efficient. The issues of breakdown point and robust tests of hypotheses are also discussed. The procedure is illustrated through simulated data and real life examples.