On unbiased Lehmann-estimators of a variance of an exponential distribution with quadratic loss function
- Autores: Jadwiga Kicinska-Slaby
- Localización: Trabajos de estadística e investigación operativa, ISSN 0041-0241, Vol. 33, Nº. 2, 1982, págs. 79-96
- Idioma: inglés
- DOI: 10.1007/bf02888624
- Títulos paralelos:
- Estimadores insesgados en el sentido de Lehmann de la varianza de una distribución exponencial con una función cuadrática de pérdidas
- Enlaces
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Resumen
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 ?-r of unknown parameter ? of gamma distribution with density f(x|?, b) = ?b-1 e-?x xb-1 / G(b), x>0, where b is a known parameter, for loss function L(?-r, ?-r) = (?-r - ?-r)2 / ?-2r.
Goodman in [1] choosing three loss functions of different shape found unbiased Lehmann-estimators, of the variance s2 of the normal distribution. In particular for quadratic loss function he took weight of the form K(s2) = C and K(s2) = (s2)-2 only.
In this work we obtained the class of all unbiased Lehmann-estimators of the variance ?2 of the exponential distribution, among estimators of the form a(n) (S1n Xi)2 -i.e. functions of the sufficient statistics- with quadratic loss function with weight of the form K(?2) = C(?2)C1, C > 0
