An Algorithm to Estimate a Nonuniform Convergence Bound in the Central Limit Theorem

Vladimir Nikulin

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arXiv · 1004.0552

An Algorithm to Estimate a Nonuniform Convergence Bound in the Central Limit Theorem

Vladimir Nikulin

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Abstract

A nonuniform version of the Berry-Esseen bound has been proved. The most important feature of the new bound is a monotonically decreasing function C(|t|) instead of the universal constant C=29.1174: C(|t|) 3.2, and C(|t|) tends to 1+e if |t| is increasing. The function C(|t|) has very complex analytical expression based on indicator functions. A general algorithm was developed in order to estimate values of C(|t|) for an arbitrary t.

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Vladimir Nikulin. 2010-04-05. An Algorithm to Estimate a Nonuniform Convergence Bound in the Central Limit Theorem. https://arxiv.org/abs/1004.0552

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