WIAS Preprint No. 2186, (2015)

Generalized Post--Widder inversion formula with application to statistics


  • Belomestny, Denis
  • Mai, Hilmar
  • Schoenmakers, John G. M.
    ORCID: 0000-0002-4389-8266

2010 Mathematics Subject Classification

  • 62G07 65R32


  • Laplace transform, inversion formula, Post-Widder formula, variance-mean mixtures, density estimation




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.

Appeared in

  • J. Math. Anal. Appl., 455 (2017) pp. 89--104.

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