Generalized Post–Widder inversion formula with application to statistics
| Autor: | John Schoenmakers, Denis Belomestny, Hilmar Mai |
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| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Laplace transform
Mean squared error Applied Mathematics Inverse transform sampling 010103 numerical & computational mathematics Density estimation 01 natural sciences Inversion (discrete mathematics) 010101 applied mathematics Mixing (mathematics) Convergence (routing) Mathematik Statistical inference Applied mathematics 0101 mathematics Analysis Mathematics |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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