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

Título inglés	On unbiased Lehmann-estimators of a variance of an exponential distribution with quadratic loss function.
Título español	Estimadores insesgados en el sentido de Lehmann de la varianza de una distribución exponencial con una función cuadrática de pérdidas.
Autor/es	Kicinska-Slaby, Jadwiga
Organización	Inst. Math. Tech. Univ. Lodz, Lodz, Polonia
Revista	0041-0241
Publicación	1982, 33 (2): 79-96, 6 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	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.
Clasificación UNESCO	120904
Palabras clave español	Inferencia estadística ; Estimador puntual
Código MathReviews	MR0697373
Código Z-Math	Zbl 0521.62021
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