Tangent measures and Lp estimation of tangent maps

Maria Mera and Manuel Morán Cabré
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Manuel Morán Cabré: Departamento de Fundamentos del Análisis Económico I (Análisis Económico). Universidad Complutense de Madrid., https://www.ucm.es//departamento-de-analisis-economico-y-economia-cuantitativa

No 96-25, Documentos de trabajo de la Facultad de Ciencias Económicas y Empresariales from Universidad Complutense de Madrid, 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.

Keywords: Lp- estimation; Tangent maps; Hausdorff measures; Tangent measures. (search for similar items in EconPapers)
Pages: 15 pages
Date: 1996
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