Lehmann in [4] has generalised the notion of the unbiased estimator with respect to the assumed loss function. In [5] Singh considered admissible estimators of function λ-r of unknown parameter λ of gamma distribution with density f(x|λ, b) = λb-1 e-λx xb-1 / Γ(b), x>0, where b is a known parameter, for loss function L(λ -r, λ-r) = (λ -r - λ-r)2 / λ-2r.
Goodman in [1] choosing three loss functions of different shape found unbiased Lehmann-estimators, of the variance σ2 of the normal distribution. In particular for quadratic loss function he took weight of the form K(σ2) = C and K(σ2) = (σ2)-2 only.
In this work we obtained the class of all unbiased Lehmann-estimators of the variance λ2 of the exponential distribution, among estimators of the form α(n) (Σ1 n Xi)2 -i.e. functions of the sufficient statistics- with quadratic loss function with weight of the form K(λ2) = C(λ2)C1 , C > 0.
@article{urn:eudml:doc:40690,
title = {On unbiased Lehmann-estimators of a variance of an exponential distribution with quadratic loss function.},
journal = {Trabajos de Estad\'\i stica e Investigaci\'on Operativa},
volume = {33},
year = {1982},
pages = {79-96},
zbl = {0521.62021},
mrnumber = {MR0697373},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40690}
}
Kicinska-Slaby, Jadwiga. On unbiased Lehmann-estimators of a variance of an exponential distribution with quadratic loss function.. Trabajos de Estadística e Investigación Operativa, Tome 33 (1982) pp. 79-96. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40690/