Sankhya: The Indian Journal of Statistics

2002, Volume 64, Series B, Pt. 2, 128--140

OUTLIER RESISTANT MINIMUM DIVERGENCE METHODS IN DISCRETE PARAMETRIC MODELS

By

AYANENDRANATH BASU, Indian Statistical Institute, Kolkata

SUMMARY. Minimum Hellinger distance and related methods have been shown to simultaneously possess first order asymptotic efficiency and attractive robustness properties (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 outlier 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.

AMS (1991) subject classification}. Primary 62F03; secondary 62F35.

Key words and phrases. Bounded effective influence, disparity, generalized hellinger divergence; influence function; residual adjustment function.

Full paper (PDF)