The use of regularization methods in computing Radon-Nikodym derivatives. Application to grain-size distributions

Claude Manté (1)

1 MIO - Institut méditerranéen d'océanologie

Let a probability law nu on [a; b] be absolutely continuous with respect to another probability law mu (specified), equivalent to the Lebesgue measure lambda on [a; b]. We seek to approximate the density d nu/d mu (assumed to be in L-mu(2) ([a; b])) in the least square sense, given the values of the distribution function nu([a; t]) at fixed points {t(j) : 1 less than or equal to j less than or equal to p}. We obtain a convenient solution of this ill-posed problem via a Hilbert space embedding, and the associated discretized problem is solved by using regularization methods. This problem is connected with sedimentological topics such as sediment transport and changes of scale. As an example, a weight frequency cumulative curve is processed.

Mots clés: measures derivation; reproducing kernels; L-curve; multivariate statistical analysis; ILL-POSED PROBLEMS

Domaines: Méthodologie [stat.ME]; Théorie [stat.TH]; Applications [stat.AP]; Interfaces continentales, environnement; Analyse numérique [math.NA]; Statistiques [math.ST]; Milieux et Changements globaux

Claude Manté. The use of regularization methods in computing Radon-Nikodym derivatives. Application to grain-size distributions. SIAM Journal on Scientific Computing, 1999, 21, pp.455-472. ⟨10.1137/S1064827597319374⟩. ⟨hal-00693392⟩