On Esseen type inequalities for combinatorial random sums

Andrei N. Frolov

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 12, 5932-5940

Abstract: We derive new bounds of the remainder in a combinatorial central limit theorem with a random number of summands. Esseen type inequalities are obtained for random combinatorial sums. Various moment conditions are considered. Moments of order 2 + δ, δ ∈ (0, 1], are partial cases. A variant of a combinatorial central limit theorem is proved for random sums with indices having Poisson distributions.

Date: 2017
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DOI: 10.1080/03610926.2015.1115074

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