Non-uniform Bounds and Edgeworth Expansions in Self-normalized Limit Theorems

Pascal Beckedorf () and Angelika Rohde ()
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Pascal Beckedorf: University of Freiburg
Angelika Rohde: University of Freiburg

Journal of Theoretical Probability, 2025, vol. 38, issue 1, 1-94

Abstract: 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 imposing only 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.

Keywords: Edgeworth expansion; Non-uniform bounds; Central limit theorem; Local limit theorem; Entropy; Total variation distance; Self-normalized sums; Student t-statistic; Rate of convergence; Primary 60F15; secondary 62E20 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10959-024-01376-8

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