| Abstrakt: |
Let X1 X2, ... be independent and identically distributed observations with probability densities p(x; θ) with respect to some measure µ0. Extending some work of Barankin and Gurland [2] we shall in this paper first give a proof of the existence of consistent, asymptotically normal distributed (c.a.n.) estimators under relative mild restrictions on the family P = p(x; θ) of probability densities. Instead of assuming, as did Barankin and Gurland, for the existence proof that socalled separators exist, we shall be able to rely on some results of differential geometry, viz. the existence of tubular neighborhoods, in carrying out the proof. In actually constructing c.a.n. estimators separators are of great use, but they are irrelevant for the general existence theorem. [ABSTRACT FROM PUBLISHER] |
