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.

翻译：基于统计散度最小化的稳健推断已被证明是经典极大似然及相关方法的有用替代。Basu等人(1998)引入了密度幂散度(DPD)族作为两个概率密度函数间差异的度量，并将其用于独立同分布数据的参数稳健估计。Ghosh等人(2017)提出了更一般的散度度量类，即S散度族，并通过若干渐近性质和数值示例讨论了其在稳健参数估计中的实用性。本文针对一般模型设定，发展了最小S散度估计量（特别是最小DPD估计量）的渐近崩溃点相关结果。本文的主要结果为这些估计量的渐近崩溃点提供了下界，该下界与数据维度无关，进而证实了它们在高维数据稳健推断中的实用性。