Asymptotic Expansions for i.i.d. Sums Via Lower-order Convolutions

Kenneth S. Berenhaut, James W. Chernesky, Jr. and Ross P. Hilton

Communications in Statistics - Theory and Methods, 2015, vol. 44, issue 11, 2330-2350

Abstract: In this article, we introduce new asymptotic expansions for probability functions of sums of independent and identically distributed random variables. Results are obtained by efficiently employing information provided by lower-order convolutions. In comparison with Edgeworth-type theorems, advantages include improved asymptotic results in the case of symmetric random variables and ease of computation of main error terms and asymptotic crossing points. The first-order estimate can perform quite well against the corresponding renormalized saddlepoint approximation and, pointwise, requires evaluation of only a single convolution integral. While the new expansions are fairly straightforward, the implications are fortuitous and may spur further related work.

Date: 2015
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DOI: 10.1080/03610926.2013.765473

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