共通域分解:在无限-高维度噪声下M-估计器的确切风险

The Conjugate Domain Dichotomy: Exact Risk of M-Estimators under Infinite-Variance Noise in High Dimensions

This paper studies high-dimensional M-estimation in the proportional asymptotic regime (p/n -> gamma > 0) when the noise distribution has infinite variance. For noise with regularly-varying tails of index alpha in (1,2), we establish that the asymptotic behavior of a regularized M-estimator is governed by a single geometric property of the loss function: the boundedness of the domain of its Fenchel conjugate. When this conjugate domain is bounded -- as is the case for the Huber, absolute