On the admissibility and inadmissibility of estimators of scale parameters using an asymmetric loss function

Estimation of the scale parameter in the Exponential and Normal families using asymmetric modified LINEX loss function are considered. The best scale-invariant estimators of the parameters of interest are obtained and their admissibility conjectured in the absence of a nuisance parameter. The admissibility and inadmissibility of the linear functions of the form cY+d, where Y ∽λΓ(n,1), are studied.