We develop a general theory for the goodness-of-fit test to non-linear models. In particular, we assume that observations are noisy samples of submanifold defined by sufficiently smooth map. The observation noise is additive Gaussian. Our main result shows “residual” model fit, solving least-square problem, follows (possibly noncentral) χ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmln...

This paper presents the Universality Argument that pleasure is goodness. It proceeds from a moral sense theory analyzes concepts as concerned with what all should hope for, feel guilty about, and admire. requires rejecting view judgment concerns empirically inaccessible norms governing action. The first premise defines goodness please all. second reduces to perceptual accuracy. third invokes st...

Classes of coordinate-invariant omnibus goodness-of-fit tests on compact Riemannian manifolds are proposed. The tests are based on Giné's Sobolev tests of uniformity. A condition for consistency is given. The tests are illustrated by an example on the rotation group SO(3). 1. Introduction. Although many tests of goodness of fit are available for distributions on the circle, comparatively little...