THE CONSISTENCY OF A SMOOTHED MINIMUM DISTANCE ESTIMATE

We give sufficient conditions for the consistency of a minimum distanc e density estimate, obtained by minimizing the L(1) distance between a kernel estimate with smoothing factor h and a density in a collection G of densities. The optimization is performed over all h > 0 and all of G. Various parametric and non-parametric target classes G are consi dered. It turns out that the choice of the kernel is crucial for the c onsistency of this minimum distance method.