Abstract:Being encouraged by [AKRS] that provides an amazing bridge between Statistics and Invariant Theory, and especially by [FM], where quiver semi-invariant techniques apply to verify the existence of MLE for a recent iPCA model, we provide an enhancement to [FM]. Our Theorem 5.2 yields necessary and sufficient conditions for MLE to exist generically for any dimension vector. The conditions can be easily checked with either of our software [T] or [FF] based on Derksen-Weyman algorithm. This simplifies the application for statistics practitioners and non-specialists in quivers. For those deep in quiver Representation Theory, Theorem 5.2 relates the MLE existence to the local semi-simplicity of representations as introduced in [Sh07]. Moreover, we implemented in [FF] the Flip-Flop algorithm from [TA] and checked that it does work in all cases guaranteed by Theorem 5.2. We hope that our elementary and short text can serve for the experts in both domains as a warm start in a new category. And we welcome practitioners to use our code at [FF] for their own experiments.
From: Dmitri Shmelkin [view email]
[v1]
Wed, 27 May 2026 18:23:10 UTC (8 KB)
[v2]
Mon, 20 Jul 2026 09:36:11 UTC (10 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。