The Double Exponential Distribution: Using Calculus to Find a Maximum Likelihood Estimator

Lehmann (1983) discussed several examples of absurd uniform minimum variance unbiased (UMVU) estimators. He argued that these estimators arose because the amount of information available was inadequate for the estimation problem at hand. Here I argue that such absurd UMVU estimators result more from the property of unbiasedness than from inadequate information.