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

Jadwiga Kicinska-Slaby

• 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