1 results
Search Results
Now showing 1 - 1 of 1
- ItemGeneralized Post-Widder inversion formula with application to statistics(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Belomestny, Denis; Mai, Hilmar; Schoenmakers, JohnIn 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.