A sharper Lyapunov–Katz central limit error bound for i.i.d. summands Zolotarev-close to normal
Year: 2025
Type: article
Abstract: We prove a central limit error bound for convolution powers of laws with finite moments of order r ∈ ] 2 , 3 ] r \in ]2,3] , taking a closeness of the laws to normality into account. Up to a universal constant, this generalises the case of r = 3 r=3 of the sharpening of the Berry (1941) – Esseen (1942) theorem obtained by Mattner (2024), namely by sharpening here the Katz (1963) error bound for the i.i.d. case of Lyapunov’s (1901) theorem. Our proof uses a partial generalisation of the theorem of Senatov and Zolotarev (1986) used for the earlier special case. A result more general than our main one could be obtained by using instead another theorem of Senatov (1980), but, unfortunately, an auxiliary inequality used in the latter’s proof is wrong.
DOI: 10.1090/tpms/1245
Authors: Lena Jonas, Lutz Mattner
Institution: Universität Trier
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416297278