Generalized Post-Widder inversion formula with application to statistics

Denis Belomestny (), Hilmar Mai () and John Schoenmakers ()
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Denis Belomestny: Duisburg-Essen University, Essen and IITP RAS
Hilmar Mai: CREST, ENSAE, ParisTech
John Schoenmakers: Weierstrass Institute

No 2015-10, Working Papers from Center for Research in Economics and Statistics

Abstract: In this work we derive an inversion formula for the Laplace transform of a density observed on a curve in the complex domain, which generalizes the well known Post-Widder formula. We establish convergence of our inversion method and derive the corresponding convergence rates for the case of a Laplace transform of a smooth density. As an application we consider the problem of statistical inference for variance-mean mixture models. We construct a nonparametric estimator for the mixing density based on the generalized Post-Widder formula, derive bounds for its root mean square error and give a brief numerical example.

Keywords: Laplace transform; inversion formula; Post-Widder formula; variancemean mixtures; density estimation. (search for similar items in EconPapers)
Pages: 18
Date: 2015-11
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