2023/04/15 by Subhrajyoty Roy, Roy, Subhrajyoty, Abir De Sarkar +5 · 2 citations
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2304.07466
openalex publication_date 2023/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.