Let $X_1, X_2, \ldots, X_k$ be $k$ independent gamma random variables with different scale parameters but with a common known shape parameter. Suppose the population corresponding to the largest $X_{(1)}$ [or the smallest $X_{(k)}$] observation is selected. The problem of estimating the scale parameter $\theta_{(1)}$ [or $\theta_{(k)}$] of the selected population is considered. We derive, using the method of differential inequalities, explicit estimators that dominate the natural or the existing estimators. The improved estimators of $\theta_{(1)}$ are similar to that of DasGupta estimators for the usual simultaneous estimation problem. An implication of this result for the simultaneous estimation of the selected subset is also considered.
Publié le : 1992-12-14
Classification:
Estimation after selection,
gamma scale parameters,
inadmissible estimators,
differential inequalities,
simultaneous estimation after selection,
62C15,
62F10,
62F07
@article{1176348913,
author = {Vellaisamy, P.},
title = {Inadmissibility Results for the Selected Scale Parameters},
journal = {Ann. Statist.},
volume = {20},
number = {1},
year = {1992},
pages = { 2183-2191},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348913}
}
Vellaisamy, P. Inadmissibility Results for the Selected Scale Parameters. Ann. Statist., Tome 20 (1992) no. 1, pp. 2183-2191. http://gdmltest.u-ga.fr/item/1176348913/