On Stein’s method for products of normal random variables and zero bias couplings

Journal article

Abstract:: In this paper we extend Stein's method to the distribution of the product of n independent mean zero normal random variables. A Stein equation is obtained for this class of distributions, which reduces to the classical normal Stein equation in the case n=1. This Stein equation motivates a generalisation of the zero bias transfor- mation. We establish properties of this new transformation, and illustrate how they may be used together with the Stein equation to assess distributional distances f...
Expand abstract
Collapse abstract

Files:: BEJ1406-008R3A0.pdf

(Preview, Accepted manuscript, pdf, 462.6KB, Terms of use)

Institution:

University of Oxford

Division:

MPLS

Department:

Statistics

Role:

Author

Funding agency for:

Gaunt, R

Keywords:: distributional transformation

products of normal random variables

zero biasing

coupling

Stein's method
Pubs id:: pubs:607657
UUID:: uuid:562e7b59-d25f-445e-8fc8-7808a965296c
Local pid:: pubs:607657
Source identifiers:: 607657
Deposit date:: 2016-03-04

Copyright holder:: Bernoulli Society
Notes:: This is the accepted manuscript version of the article. The final version is available online from Bernoulli Society for Mathematical Statistics and Probability at: 10.3150/16-BEJ848

Licence:: Terms and Conditions of Use for Oxford University Research Archive

If you are the owner of this record, you can report an update to it here: Report update to this record