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

By Robert E. Gaunt. 2013

49 citations recorded by the source corpus.

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 transformation. We establish properties of this new transformation, and illustrate how they may be used together with the Stein equation to assess distributional distances for statistics that are asymptotically distributed as the product of independent central normal random variables. We end by proving some product normal approximation theorems.

Subfields: Algebra and Number Theory, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3f1d06da15ed3ef672992214f6e68c23b820285d

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In Algebra and Number Theory

In Statistical and Nonlinear Physics

In Statistics and Probability

Citations in the corpus

Stein's method for comparison of univariate distributions (2014, methodology): “Outside of the Gaussian and Poisson frameworks, for univariate distributions the method has now also been shown to be effective for: exponential approximation [19, 79], Gamma approximation [68, 81, 70], binomial approximation [31], Beta approximation [43, 28], the asymptotics of rank distributions [”