发表机构
KU Leuven; UCLouvain（荷语鲁汶大学; 法语鲁汶大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对Fréchet回归模型，提出无约束条件最大似然估计，证明其在非紧参数空间上的一致性和渐近正态性，并通过宇宙闭包实现参数空间紧化。
AI 中文摘要
重尾响应变量通常被建模为协变量的函数，但现有的最大似然估计量的渐近理论通过将参数限制在一个紧集上来规避某些技术困难，而该紧集并非自然的参数空间。我们考虑一个Fréchet模型，其尺度参数对数线性地依赖于协变量向量，而尾部参数为常数，并联合研究尾部参数和回归系数的条件最大似然估计量。我们证明该估计量在完整非紧参数空间上是一致的，并且是渐近正态的，其极限协方差矩阵为Fisher信息矩阵的逆。一致性是通过依赖于欧几里得空间的宇宙闭包的特定参数空间紧化获得的。为完成该步骤所需的Wald一致性定理的推广，从单个观测到观测块，在抽象框架中陈述，并可能具有独立的研究价值。
英文摘要
Heavy-tailed response variables are routinely modeled as a function of covariates, but the asymptotic theory available for the resulting maximum likelihood estimators sidesteps certain technical difficulties by restricting the parameters to a compact set, which is not the natural parameter space. We consider a Fréchet model whose scale parameter depends log-linearly on a vector of covariates, while the tail parameter is constant, and we study the conditional maximum likelihood estimator of the tail parameter and the regression coefficients jointly. We show that this estimator is consistent over the full, noncompact parameter space, and that it is asymptotically normal, with the inverse Fisher information as limiting covariance matrix. Consistency is obtained by a specific compactification of the parameter space relying on the cosmic closure of Euclidean space. The extension of Wald's consistency theorem needed for that step, from single observations to blocks of observations, is stated in an abstract setting and is possibly of independent interest.
Comments40 pages,1 figure
