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

Probability 2011-12-30 v1

Abstract

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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Cite

@article{arxiv.1112.5719,
  title  = {An isometric study of the Lindeberg-Feller CLT via Stein's method},
  author = {Ben Berckmoes and Bob Lowen and Jan Van Casteren},
  journal= {arXiv preprint arXiv:1112.5719},
  year   = {2011}
}

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19 pages