局部渐近极小极大风险的公理化

中文摘要 AI 辅助

局部渐近极小极大（LAM）风险是统计学和计量经济学中一个基础性的效率准则。文献中使用了两种LAM风险的定义：一种出现在经典下界中，另一种出现在论证这些下界可达性的论证中。传统的效率论证与这两种定义的任何依赖于估计量的加权平均一致，因此无法揭示这些广义的$\alpha$-LAM风险指数中哪一个描述了研究者的实际偏好。我们采取决策理论的方法来系统地解决这一模糊性。我们对具有广义$\alpha$-LAM表示的一类偏好进行了公理化刻画，并证明了此类偏好可能违反基本理性要求，如单调性。受此启发，我们对具有常数权重表示的子集进行了公理化刻画。在这一类中，样本不确定性厌恶公理唯一地选择了可达性LAM。我们认为样本不确定性厌恶在规范上具有吸引力，因此我们推荐将可达性LAM作为LAM风险的功能形式。

英文摘要

Local asymptotic minimax (LAM) risk is a foundational efficiency criterion in statistics and econometrics. The literature uses two definitions of LAM risk: one which appears in classical lower bounds and another which appears in arguments establishing attainment of those bounds. Conventional efficiency arguments are consistent with any estimator-dependent weighted average of the two, and consequently do not reveal which of these generalized $α$-LAM risk indices describes researchers' actual preferences. We take a decision-theoretic approach to systematically resolve this ambiguity. We axiomatically characterize the set of preferences with a generalized $α$-LAM representation, and we document that such preferences may violate basic rationality requirements such as Monotonicity. Motivated by this, we axiomatically characterize the subset with constant-weight representations. Within this class, a Sample Uncertainty Aversion axiom uniquely selects attainment LAM. We argue that Sample Uncertainty Aversion is normatively appealing, and we therefore recommend attainment LAM as the functional form for LAM risk.

发表机构

• MIT Department of Economics（麻省理工学院经济学系）
• MIT（麻省理工学院）

机构由 AI 辅助整理，请以论文原文为准。