Tangent measures and Lp estimation of tangent maps
ISSN: 2255-5471
Year of publication: 1996
Issue: 25
Type: Working paper
More publications in: Documentos de trabajo de la Facultad de Ciencias Económicas y Empresariales
Abstract
We analyze under what conditions the best Lp- linear fittings of the action of a mapping f on small balls give reliable estimates of the tangent map Df. We show that there is an inverse relationslúp between the conditions on the regularity, in terms of local densities, of the underlying measure and the smoothness of the mapping f which are required to ensure the goodness of the estimates. The above results can be applied to the estimation of tangent maps in two empirical settings: from fiuite samples of a given probability distribution on mn and from fiuite orbits of smooth dynamical systems.