Abstract:Recent years have witnessed much progress on Gaussian and bootstrap approximations to the distribution of sums of independent random vectors with dimension $d$ large relative to the sample size $n$. However, for any number of moments $m>2$ that the summands may possess, there exist distributions such that these approximations break down if $d$ grows faster than the polynomial barrier $n^{\frac{m}{2}-1}$. In this paper, we establish Gaussian and bootstrap approximations to the distributions of winsorized and trimmed means that allow $d$ to grow at an exponential rate in $n$ as long as $m>2$ moments exist. The approximations remain valid under some amount of adversarial contamination. Our implementations of the winsorized and trimmed means do not require knowledge of $m$. As a consequence, the approximation guarantees ``adapt'' to $m$.
From: David Preinerstorfer [view email]
[v1]
Fri, 11 Apr 2025 10:51:00 UTC (28 KB)
[v2]
Tue, 3 Jun 2025 14:11:44 UTC (29 KB)
[v3]
Thu, 6 Nov 2025 10:46:29 UTC (30 KB)
[v4]
Thu, 26 Mar 2026 15:00:53 UTC (554 KB)
[v5]
Mon, 29 Jun 2026 14:40:14 UTC (556 KB)
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