On Stein’s method for products of normal random variables and zero bias couplings
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 gener...
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| Format: | Journal article |
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Bernoulli Society for Mathematical Statistics and Probability
2017
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| Sažetak: | 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 for statistics that are asymptotically distributed as the product of independent central normal random variables. |
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