Mathematics > Statistics Theory
[Submitted on 18 Aug 2024 (v1), last revised 9 Sep 2024 (this version, v2)]
Title:Approximate independence of permutation mixtures
View PDF HTML (experimental)Abstract:We prove bounds on statistical distances between high-dimensional exchangeable mixture distributions (which we call permutation mixtures) and their i.i.d. counterparts. Our results are based on a novel method for controlling $\chi^2$ divergences between exchangeable mixtures, which is tighter than the existing methods of moments or cumulants. At a technical level, a key innovation in our proofs is a new Maclaurin-type inequality for elementary symmetric polynomials of variables that sum to zero and an upper bound on permanents of doubly-stochastic positive semidefinite matrices. Our results imply a de Finetti-style theorem (in the language of Diaconis and Freedman, 1987) and general asymptotic results for compound decision problems, generalizing and strengthening a result of Hannan and Robbins (1955).
Submission history
From: Yanjun Han [view email][v1] Sun, 18 Aug 2024 03:23:12 UTC (58 KB)
[v2] Mon, 9 Sep 2024 13:58:44 UTC (60 KB)
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