An isometric study of the Lindeberg-Feller central limit theorem via Stein%26apos;s method

作者：Berckmoes B; Lowen R^*; Van Casteren J

来源：Journal of Mathematical Analysis and Applications, 2013, 405(2): 484-498.

DOI：10.1016/j.jmaa.2013.04.012

• Approach structure
• Distance
• Limit
• Weak topology
• Probability measure
• Law
• Random variable
• Central limit theorem
• Lindeberg condition
• Kolmogorov metric
• Triangular array

We use Stein%26apos;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.

• 出版日期2013-9-15