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 our software [T] based on Derksen-Weyman algorithm and simplifying 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]. We also hope that our elementary and short text can serve for the experts in both domains as a warm start in a new category.

翻译：受[AKRS]在统计学与不变量理论之间建立的桥梁启发，特别是[FM]利用箭图半不变技术验证了新型iPCA模型的最大似然估计存在性，我们提出了对[FM]的改进方法。定理5.2给出了任意维度向量下最大似然估计泛型存在的充要条件。基于Derksen-Weyman算法开发的软件[T]可便捷验证该条件，从而简化统计实践者与非箭图专业人员的应用门槛。对于深入研究箭图表示理论的学者，定理5.2揭示了最大似然估计存在性与[Sh07]提出的表示局部半单性之间的内在联系。我们期待这份简洁的基础性文本能为两个领域的专家提供跨学科研究的初步切入点。