Abstract: | Suppose that a density fθ (x) belongs to an exponential family, but that inference about θ must be based on data that are obtained from a density that is proportional to W(x)fθ(x). The authors study the Fisher information about θ in observations obtained from such weighted distributions and give conditions under which this information is greater than under the original density. These conditions involve the hazard- and reversed-hazard-rate functions. |