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Generalized Post-Widder inversion formula with application to statistics

Author

Listed:
  • Denis Belomestny

    (Duisburg-Essen University, Essen and IITP RAS)

  • Hilmar Mai

    (CREST, ENSAE, ParisTech)

  • John Schoenmakers

    (Weierstrass Institute)

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.

Suggested Citation

  • Denis Belomestny & Hilmar Mai & John Schoenmakers, 2015. "Generalized Post-Widder inversion formula with application to statistics," Working Papers 2015-10, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2015-10
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    References listed on IDEAS

    as
    1. N. H. Bingham & Rudiger Kiesel, 2002. "Semi-parametric modelling in finance: theoretical foundations," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 241-250.
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