Some inequalities related to the Stam inequality
Applications of Mathematics (2008)
- Volume: 53, Issue: 3, page 195-205
- ISSN: 0862-7940
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topKagan, Abram, and Yu, Tinghui. "Some inequalities related to the Stam inequality." Applications of Mathematics 53.3 (2008): 195-205. <http://eudml.org/doc/37778>.
@article{Kagan2008,
abstract = {Zamir showed in 1998 that the Stam classical inequality for the Fisher information (about a location parameter) \[ 1/I(X+Y)\ge 1/I(X)+1/I(Y) \]
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.},
author = {Kagan, Abram, Yu, Tinghui},
journal = {Applications of Mathematics},
keywords = {Fisher information; location parameter; Pitman estimators; Fisher information; location parameter; Pitman estimators},
language = {eng},
number = {3},
pages = {195-205},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some inequalities related to the Stam inequality},
url = {http://eudml.org/doc/37778},
volume = {53},
year = {2008},
}
TY - JOUR
AU - Kagan, Abram
AU - Yu, Tinghui
TI - Some inequalities related to the Stam inequality
JO - Applications of Mathematics
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 3
SP - 195
EP - 205
AB - Zamir showed in 1998 that the Stam classical inequality for the Fisher information (about a location parameter) \[ 1/I(X+Y)\ge 1/I(X)+1/I(Y) \]
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.
LA - eng
KW - Fisher information; location parameter; Pitman estimators; Fisher information; location parameter; Pitman estimators
UR - http://eudml.org/doc/37778
ER -
References
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