Asymptotic distribution and robustness of minimum total variation distance estimators

摘要

This paper considers the problem of deducing the asymptotic distribution of minimum total variation distance estimators based on grouped data. Under suitable assumptions the limit distributions of these estimators are shown to be the distributions of the minimizers of well defined random functions. Moreover, an explicit form of these laws is given when the parameter space is a subset of the real line. Finally, these estimators are compared, from the point of view of robustness, with other minimum g-divergence estimators and their superiority is stressed.