Lam, H., Blanchet, J., Burch, D. et al. Corrections to the Central Limit Theorem for Heavy-tailed Probability Densities. J Theor Probab 24, 895–927 (2011). https://doi.org/10.1007/s10959-011-0379-y
Abstract
Classical Edgeworth expansions provide asymptotic correction terms to the Central Limit Theorem (CLT) up to an order that depends on the number of moments available. In this paper, we provide subsequent correction terms beyond those given by a standard Edgeworth expansion in the general case of regularly varying distributions with diverging moments (beyond the second). The subsequent terms can be expressed in a simple closed form in terms of certain special functions (Dawson’s integral and parabolic cylinder functions), and there are qualitative differences depending on whether the number of moments available is even, odd, or not an integer, and whether the distributions are symmetric or not. If the increments have an even number of moments, then additional logarithmic corrections must also be incorporated in the expansion parameter. An interesting feature of our correction terms for the CLT …
Authors
Henry Lam, Jose Blanchet, Damian Burch, Martin Z Bazant
Publication date
2011/12
Journal
Journal of Theoretical Probability
Volume
24
Pages
895-927
Publisher
Springer US
