On close relations of local likelihood density estimation

Recent papers of Copas (1995), Hjort and Jones (1996) and Loader (1996) have developed closely related methods for “local likelihood” density estimation. In various places, however, a more “simple-minded” and explicit analogue of local polynomial fitting in regression has been proposed for density estimation. By introducing the usual kind of binning procedure into Hjor and Jones' method, it is shown how the more and less sophisticated versions can be reconciled. Also, we attempt to understand better the role of the attractive subclass of local likelihood methodology proposed by Loader. Finally, we look at a further subset of methods and make some theoretical comparisons between members of this class