Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4616319 | Journal of Mathematical Analysis and Applications | 2013 | 15 Pages |
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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Physical Sciences and Engineering
Mathematics
Analysis
Authors
B. Berckmoes, R. Lowen, J. Van Casteren,