Category: Fréchet-Darmois-Cramèr-Rao bound

Fisher’s lost information

After a post on X validated and a good discussion at work, I came to the conclusion [after many years of sweeping the puzzle under the carpet] that the (a?) Fisher information obtained for the Uniform distribution U(0,θ) as θ⁻¹ is meaningless. Indeed, there are many arguments: The lack of derivability of the indicator function […]

efficiency and the Fréchet-Darmois-Cramèr-Rao bound

  Following some entries on X validated, and after grading a mathematical statistics exam involving Cramèr-Rao, I came to wonder at the relevance of the concept of efficiency outside [and even inside] the restricted case of unbiased estimators. The general (frequentist) version is that the variance of an estimator δ of [any transform of] θ […]