最优分配与曲面下体积

中文摘要 AI 辅助

本文开发了一个用于估计和推断关键函数集的投影集合体积的框架，特别关注最优接收者操作特征（ROC）曲面下的凸体。具体而言，我们提出了一种体积计算方法，该方法首先使用Aumann期望表示，然后应用Minkowski混合体积。利用这一框架，我们证明了ROC曲面下总体体积（VUS）与对称U统计量核的期望成正比。随后，我们提出了一种双重/去偏机器学习估计量用于VUS，推导了其渐近性质，并开发了推断程序。该框架的进一步应用包括对预定义组间可行误差集的分析，以及用于衡量不平等的基尼系数的自然推广。

英文摘要

This paper develops a framework for estimation and inference on the volumes of sets that are projections of critical function sets, focusing particularly on the convex body beneath the optimal receiver operating characteristic (ROC) surface. Specifically, we propose a volume calculation method that first uses an Aumann expectation representation and then applies Minkowski mixed volumes. Using this framework, we show that the population volume under the ROC surface (VUS) is proportional to the expectation of a symmetric U-statistic kernel. We then propose a double/debiased machine learning estimator of the VUS, derive its asymptotic properties, and develop an inference procedure. Further applications of this framework include an analysis of the feasible error set across pre-defined groups and a natural generalization of the Gini coefficient for measuring inequality.

发表机构

• School of Finance, Renmin University of China（中国人民大学财政金融学院）
• Department of Economics, Stanford University（斯坦福大学经济学系）
• Department of Economics, University of California Santa Cruz（加州大学圣克鲁兹分校经济学系）
• School of Economics and Management, Beijing Jiaotong University（北京交通大学经济管理学院）

机构由 AI 辅助整理，请以论文原文为准。