On unbiased Lehmann-estimators of a variance of an exponential distribution with quadratic loss function.

Kicinska-Slaby, Jadwiga. "On unbiased Lehmann-estimators of a variance of an exponential distribution with quadratic loss function.." Trabajos de Estadística e Investigación Operativa 33.2 (1982): 79-96. <http://eudml.org/doc/40690>.

@article{Kicinska1982,
abstract = {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&gt;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) (Σ1n Xi)2 -i.e. functions of the sufficient statistics- with quadratic loss function with weight of the form K(λ2) = C(λ2)C1, C &gt; 0.},
author = {Kicinska-Slaby, Jadwiga},
journal = {Trabajos de Estadística e Investigación Operativa},
keywords = {Inferencia estadística; Estimador puntual; unbiased Lehmann-estimators of variance; exponential distribution; minimum of risk; geometric interpretations},
language = {eng},
number = {2},
pages = {79-96},
title = {On unbiased Lehmann-estimators of a variance of an exponential distribution with quadratic loss function.},
url = {http://eudml.org/doc/40690},
volume = {33},
year = {1982},
}

TY - JOUR
AU - Kicinska-Slaby, Jadwiga
TI - On unbiased Lehmann-estimators of a variance of an exponential distribution with quadratic loss function.
JO - Trabajos de Estadística e Investigación Operativa
PY - 1982
VL - 33
IS - 2
SP - 79
EP - 96
AB - 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&gt;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) (Σ1n Xi)2 -i.e. functions of the sufficient statistics- with quadratic loss function with weight of the form K(λ2) = C(λ2)C1, C &gt; 0.
LA - eng
KW - Inferencia estadística; Estimador puntual; unbiased Lehmann-estimators of variance; exponential distribution; minimum of risk; geometric interpretations
UR - http://eudml.org/doc/40690
ER -