OUTLIER RESISTANT MINIMUM DIVERGENCE METHODS IN DISCRETE PARAMETRIC MODELS By AYANENDRANATH BASU

SUMMARY. Minimum Hellinger distance and related methods have been shown to simultaneously possess first order asymptotic efficiency and attractive robustness proper-ties (Beran 1997; Simpson 1987, 1989a; Lindsay 1994). It has been noted, however, that these minimum divergence procedures are generally associated with unbounded influence functions, a property considered undesirable in traditional robust procedures. Lindsay has demonstrated the limitations of the influence function approach in this case. Following Lindsay’s outlier stability approach, we show in this paper that there exists a similar out-lier resistance property for the corresponding tests of hypotheses, and that this outlier resistance property leads to some useful and interesting results for the estimators and the corresponding tests of hypotheses for the generalized Hellinger divergence family (Simpson 1989b; Basu et al., 1997) in discrete models