In the context of a single equation in a system of simultaneous equations there is evidently some confusion in the literature as to the correct approach to the problem of prediction. Here we explore this problem and compare three different approaches to it. We also relate this discussion to...

Abstract Some linkages between kernel and penalty methods of density estimation are explored. It is recalled that classical Gaussian kernel density estimation can be viewed as the solution of the heat equation with initial condition given by data. We then observe that there is a direct...