Non-uniform bounds and Edgeworth expansions in self-normalized limit theorems

zbMATH Open1498.60004arXiv2207.14402MaRDI QIDQ5051306

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Publication date: 22 November 2022

Abstract: We study Edgeworth expansions in limit theorems for self-normalized sums. Non-uniform bounds for expansions in the central limit theorem are established while only imposing minimal moment conditions. Within this result, we address the case of non-integer moments leading to a reduced remainder. Furthermore, we provide non-uniform bounds for expansions in local limit theorems. The enhanced tail-accuracy of our non-uniform bounds allows for deriving an Edgeworth-type expansion in the entropic central limit theorem as well as a central limit theorem in total variation distance for self-normalized sums.

Full work available at URL: https://arxiv.org/abs/2207.14402

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