  Robust inference based on the minimization of statistical divergences has
proved to be a useful alternative to classical techniques based on maximum
likelihood and related methods. Basu et al. (1998) introduced the density power
divergence (DPD) family as a measure of discrepancy between two probability
density functions and used this family for robust estimation of the parameter
for independent and identically distributed data. Ghosh et al. (2017) proposed
a more general class of divergence measures, namely the S-divergence family and
discussed its usefulness in robust parametric estimation through several
asymptotic properties and some numerical illustrations. In this paper, we
develop the results concerning the asymptotic breakdown point for the minimum
S-divergence estimators (in particular the minimum DPD estimator) under general
model setups. The primary result of this paper provides lower bounds to the
asymptotic breakdown point of these estimators which are independent of the
dimension of the data, in turn corroborating their usefulness in robust
inference under high dimensional data.
