A GENERALIZATION OF THE MOVING MEAN

We have extended the concept of the moving mean in two ways. We first show how to incorporate nearby points, in a natural way, that automatically determines the weight function. This weighting can also probe all scale-lengths of the data. We further extend this to include both isotropic and anisotropic sampling in N-dimensional space. We also generalize to include alternative weightings, specified by the user of the technique, and solve the general, N-dimensional, isotropic problem. We make no unverifiable assumptions regarding the errors of observation nor of the form of the moving mean. A numerical example is included too.