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Variance-Gamma approximation via Stein's method

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Variance-Gamma approximation via Stein's method
2.	Creator	Author's name, affiliation, country	Robert Edward Gaunt; University of Oxford; United Kingdom
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Stein's method; Variance-Gamma approximation; rates of convergence
3.	Subject	Subject classification	60F05
4.	Description	Abstract	Variance-Gamma distributions are widely used in financial modelling 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 $\sum_{i,j,k=1}^{m,n,r}X_{ik}Y_{jk}$, where the $X_{ik}$ and $Y_{jk}$ 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.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	EPSRC
7.	Date	(YYYY-MM-DD)	2014-03-29
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/3020
10.	Identifier	Digital Object Identifier	10.1214/EJP.v19-3020
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 19
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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