Generalized Post-Widder inversion formula with application to statistics
Statistics Theory
2015-12-01 v1 Statistics Theory
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.
Cite
@article{arxiv.1511.09298,
title = {Generalized Post-Widder inversion formula with application to statistics},
author = {Denis Belomestny and Hilmar Mai and John Schoenmakers},
journal= {arXiv preprint arXiv:1511.09298},
year = {2015}
}