DIFFERENTIABILITY OF LIKELIHOOD RATIOS WITH RATES
Abstract: Call a function if the difference quotient
approximates the derivative at this rate. Consider some root of the density of a one-parameter
family of probability measures as a function of the parameter. We characterize
differentiability of this root in some (not necessarily corresponding) mean at a certain
rate by an appropriate differentiability of an arbitrary other root at the same rate.
In particular, we characterize Hellinger differentiability at some rate in terms of
differentiability of the densities. This allows us to compare Hellinger differentiability at some
rate with a differentiability concept of Pfanzagl and Wefelmeyer [11], which is
necessary and sufficient for local asymptotic normality in the i.i.d. case at a certain rate.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -