Abstract
Continuing the consideration of the independent case, Chap. 8 presents non-uniform bounds for sums of independent random variables. In particular, by use of non-uniform concentration inequalities and the Bennett–Hoeffding inequality, bounds for the absolute difference between the distribution function F(z) of a sum of independent variables and the normal Φ(z), which may depend on z∈ℝ, are provided. Non-uniform bounds serve as a counterpoint to the earlier derived supremum norm bounds that are not allowed to vary with z, and give information on how the quality of the normal approximation varies over ℝ.
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© 2011 Springer-Verlag Berlin Heidelberg
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Chen, L.H.Y., Goldstein, L., Shao, QM. (2011). Non-uniform Bounds for Independent Random Variables. In: Normal Approximation by Stein’s Method. Probability and Its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15007-4_8
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DOI: https://doi.org/10.1007/978-3-642-15007-4_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15006-7
Online ISBN: 978-3-642-15007-4
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