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arXiv · 1511.09298

Generalized Post-Widder inversion formula with application to statistics

Denis Belomestny·Hilmar Mai·John Schoenmakers
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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.

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Denis Belomestny, Hilmar Mai, John Schoenmakers. 2015-11-30. Generalized Post-Widder inversion formula with application to statistics. https://arxiv.org/abs/1511.09298

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