This note presents a simple and locally optimal test statistic for the Pareto law. The test is based on the Lagrange multiplier principle and can be computed easily once the maximum likelihood estimator of the scale parameter of the Pareto density has been obtained. A Monte Carlo exercise shows...

This note extends the standard kernel density estimator to the case of weighted samples in several ways. In the first place I consider the obvious extension by substituting the simple sum in the definition of the estimator by a weighted sum, but I also consider other alternatives of introducing...