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Reference: Gaunt, RE, (2014). Variance-Gamma approximation via Stein's method. Electronic Journal of Probability, 19 (0), 1-33.Citable link to this page:

 

Variance-Gamma approximation via Stein's method

Abstract: Variance-Gamma distributions are widely used in financial modeling and contain as special cases the normal, Gamma and Laplace distributions. In this paper we extend Stein's method to this class of distributions. In particular, we obtain a Stein equation and smoothness estimates for its solution. This Stein equation has the attractive property of reducing to the known normal and Gamma Stein equations for certain parameter values. We apply these results and local couplings to bound the distance between sums of the form XikYjk, where the Xik and Yjk are independent and identically distributed random variables with zero mean, by their limiting Variance-Gamma distribution. Through the use of novel symmetry arguments, we obtain a bound on the distance that is of order m-1 + n-1 for smooth test functions. We end with a simple application to binary sequence comparison.

Peer Review status:Peer reviewedPublication status:PublishedVersion:Publisher's version Funder: Engineering and Physical Sciences Research Council   Notes:This work is licensed under a Creative Commons Attribution 3.0 License.

Bibliographic Details

Publisher: Institute of Mathematical Statistics

Publisher Website: http://imstat.org/en/index.html

Journal: Electronic Journal of Probabilitysee more from them

Publication Website: http://www.math.washington.edu/~ejpecp/

Issue Date: 2014-03-29

pages:1-33Identifiers

Urn: uuid:fa4e5187-1436-4822-837d-ee020b215a22

Source identifier: 561692

Eissn: 1083-6489

Doi: https://doi.org/10.1214/EJP.v19-3020

Issn: 1083-6489 Item Description

Type: Journal article;

Version: Publisher's versionKeywords: Stein's method Variance-Gamma approximation rates of convergence Tiny URL: pubs:561692

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Author: Gaunt, RE - institutionUniversity of Oxford Oxford, MPLS, Statistics - - - - Bibliographic Details Publisher: Institute of Mathem

Source: https://ora.ox.ac.uk/objects/uuid:fa4e5187-1436-4822-837d-ee020b215a22



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