Abstract
Necessary and sufficient conditions for the attainments of the Borovkov–Sakhanenko and the van Trees information bounds are given when the underlying distribution is an exponential family and the conjugate prior, and the estimand is a function of the parameter. Moreover, the attainments under the Jeffreys prior are also considered. Furthermore, some examples are given.
AMS 2010 SUBJECT CLASSIFICATION:
Acknowledgments
The author thanks the referee for the helpful comments and suggestions.
Notes
1 If and
are linearly dependent, then the conjugate prior of (6) cannot be expressed uniquely.
2 If a random variable p is distributed according to beta distribution the logit-transformed random variable
is distributed according to (34), and this distribution is a version of beta prime distribution (Johnson, Kotz, and Balakrishnan Citation1995).