Geodesic
On estimation of a location parameter in presence of an ancillary component
Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 1, pp. 172-176 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

If $(X, Y)$ is an observation with distribution function $F(x-\theta,y)$, $\sigma^{2}=\textrm{var}(X)$, $\rho=\textrm{corr}(X,Y)$ and $I$ is the Fisher information on $\theta$ in $(X,Y)$, then $I\ge\{\sigma^2(1-\rho^2)\}^{-1}$. The equality sign holds under conditions closely related to the conditions for linearity of the Pitman estimator of $\theta$ from a sample from $F(x-\theta,y)$. The results are extensions of earlier results for the case when only the informative component $X$ is observed.
Keywords: Fisher information, Pitman estimator. 
@article{TVP_2005_50_1_a11,
     author = {A. M. Kagan and C. R. Rao},
     title = {On estimation of a location parameter in presence of an ancillary component},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {172--176},
     year = {2005},
     volume = {50},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2005_50_1_a11/}
}
TY  - JOUR
AU  - A. M. Kagan
AU  - C. R. Rao
TI  - On estimation of a location parameter in presence of an ancillary component
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2005
SP  - 172
EP  - 176
VL  - 50
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TVP_2005_50_1_a11/
LA  - en
ID  - TVP_2005_50_1_a11
ER  - 
%0 Journal Article
%A A. M. Kagan
%A C. R. Rao
%T On estimation of a location parameter in presence of an ancillary component
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2005
%P 172-176
%V 50
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_2005_50_1_a11/
%G en
%F TVP_2005_50_1_a11
A. M. Kagan; C. R. Rao. On estimation of a location parameter in presence of an ancillary component. Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 1, pp. 172-176. http://geodesic.mathdoc.fr/item/TVP_2005_50_1_a11/

[1] Khyuber P., Robastnost v statistike, Mir, M., 1984, 512 pp. | MR

[2] Kagan A. M., Linnik Yu. V., Rao C. R., “On a characterization of the normal law based on a property of the sample average”, Sankhyā, A27 (1965), 405–406 | MR

[3] Kagan A. M., Linnik Yu. V., Pao S. R., Kharakterizatsionnye zadachi matematicheskoi statistiki, Nauka, M., 1972, 656 pp. | MR

[4] Lukach E., Kharakteristicheskie funktsii, Nauka, M., 1979, 423 pp. | MR

[5] Rao C. R., “Minimum variance estimation in distributions admitting ancillary statistics”, Sankhyā, A12 (1952), 53–56 | MR