An isometric study of the Lindeberg-Feller CLT via Stein's method

Details An isometric study of the Lindeberg-Feller CLT via Stein's method An isometric study of the Lindeberg-Feller CLT via Stein's method

2011-12-24

arxiv.org/abs/1112.5719v1

Mathematics

Probability

19 pages

Scientific paper

We use Stein's method to prove a generalization of the Lindeberg-Feller CLT providing an upper and a lower bound for the superior limit of the Kolmogorov distance between a normally distributed random variable and the rowwise sums of a rowwise independent triangular array of random variables which is asymptotically negligible in the sense of Feller. A natural example shows that the upper bound is of optimal order. The lower bound improves a result by Andrew Barbour and Peter Hall.

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