On the Role of Semielasticity in Statistics

Abstract

Assun¸cão showed that the lower bound for the mean squared relative error (MSRE) of an unbiased estimator can be expressed in terms of elasticity, thus providing a meaningful interpretation of the MSRE lower bound. Where the MSE is preferred to MSRE, however, the idea of elasticity does not apply and must be replaced by semielasticity. In this article, we restate the Fisher information measure, the Cramér-Rao lower bound, and the identification problem in terms of semielasticity.

KEY WORDS :

• Cramér-Rao inequality
• Elasticity
• Fisher information
• Identification