Generalized Post-Widder inversion formula with application to statistics

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:455

Article

Belomestny, Denis^1,2  Mai, Hilmar³  Schoenmakers, John⁴ 

[1] Duisburg Essen Univ, Duisburg, Germany

[2] Natl Res Univ Higher Sch Econ, Moscow, Russia

[3] CREST ENSAE ParisTech, Paris, France

[4] Weierstrass Inst, Berlin, Germany

关键词: Laplace transform;    Inversion formula;    Post-Widder formula;    Variance-mean mixtures;    Density estimation;   

DOI  :  10.1016/j.jmaa.2017.05.042

来源: Elsevier

【 摘 要 】

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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free