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

2022/07/28 by Pascal Beckedorf, Beckedorf, Pascal, Angelika Rohde +1 · 1 citation
Decision Sciences · Mathematics · #Probabilistic and Robust Engineering Design #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.2207.14402

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.

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