无凸性全局极小的几乎处处唯一性
Almost Sure Uniqueness of a Global Minimum Without Convexity
摘要：
本文证明了随机目标函数的argmin几乎必然唯一。本文首先给出了一个一般性结果，证明了目标函数不凸的几乎处处唯一性。一般的结果，然后适用于各种统计应用。讨论了M-估计的四个应用，包括经典似然估计和惩罚似然估计的唯一性，以及argmin定理的两个应用，阈值回归和弱识别。
英文摘要：
This paper establishes the argmin of a random objective function to be unique almost surely. This paper first formulates a general result that proves almost sure uniqueness without convexity of the objective function. The general result is then applied to a variety of applications in statistics. Four applications are discussed, including uniqueness of M-estimators, both classical likelihood and penalized likelihood estimators, and two applications of the argmin theorem, threshold regression and weak identification.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
