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

Trabajos de Estadística e Investigación Operativa (1982)

- Volume: 33, Issue: 2, page 79-96
- ISSN: 0041-0241

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topKicinska-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>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 > 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>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 > 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 -

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