Titlebook: Normal Approximation by Stein’s Method; Louis H.Y. Chen,Larry Goldstein,Qi-Man Shao Textbook 2011 Springer-Verlag GmbH Berlin Heidelberg 2

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Introduction,e introduced here, in particular, the Stein identity and the Stein equation. To convey the flavor of the method, the ‘leave one out’ coupling used in Stein’s original paper is reviewed, and compared to the more classical approach of Lindberg. A detailed outline, summary, and chapter dependency diagr

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,, Bounds,s are presented for illustration. First considering independent random variables, an .. Berry–Esseen bound is shown, followed by a demonstration of a type of contraction principle ‘toward the normal.’ Bounds in .. are then proved for hierarchical structures, that is, self similar, fractal type objec

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,, by Bounded Couplings,ed between an auxiliary random variable . and the variable .. Important cases considered include when the variable . has the same distribution as ., or has the zero bias or size bias distribution of .. The bounds shown in this chapter are often interpretable, sometimes directly, as a distance betwee

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,Non-uniform Bounds for Independent Random Variables,use of non-uniform concentration inequalities and the Bennett–Hoeffding inequality, bounds for the absolute difference between the distribution function .(.) of a sum of independent variables and the normal Φ(.), which may depend on .∈ℝ, are provided. Non-uniform bounds serve as a counterpoint to th

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