Abstract :
This paper considers parametric estimation problems with independent, identically
nonregularly distributed data. It focuses on rate efficiency, in the sense of maximal
possible convergence rates of stochastically bounded estimators, as an optimality
criterion, largely unexplored in parametric estimation. Under mild conditions, the
Hellinger metric, defined on the space of parametric probability measures, is shown
to be an essentially universally applicable tool to determine maximal possible convergence
rates. These rates are shown to be attainable in general classes of parametric
estimation problems.
