Abstract
Zamir showed in 1998 that the Stam classical inequality for the Fisher information (about a location parameter) $$ 1/I(X + Y) \geqslant 1/I(X) + 1/I(Y) $$ for independent random variables X, Y is a simple corollary of basic properties of the Fisher information (monotonicity, additivity and a reparametrization formula). The idea of his proof works for a special case of a general (not necessarily location) parameter. Stam type inequalities are obtained for the Fisher information in a multivariate observation depending on a univariate location parameter and for the variance of the Pitman estimator of the latter.
Full Text
Submitted Version (
Free)
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call