Title: On the Hodges-Lehmann estimator in a location mixture model
Authors: Fadoua Balabdaoui - ETH Zurich (Switzerland) [presenting]
Abstract: The aim is to derive the exact limit distribution of the Hogdes-Lehmann estimator, considered in the semi-parametric model of a location mixture of symmetric distributions. We give sufficient conditions on the true symmetric component for the weak convergence to hold. As already expected, the limit distribution is that of a three-dimensional centered Gaussian distribution. The variance-covariance matrix can be calculated using the known covariance structure of a standard Brownian Bridge. The examples we used to illustrate the theory indicate that the estimator is not to be advocated when the mixture components are not well separated.