The linear Fisher market (LFM) is a basic equilibrium model from economics, which also has applications in fair and efficient resource allocation. First-price pacing equilibrium (FPPE) is a model capturing budget-management mechanisms in first-price auctions. In certain practical settings such as advertising auctions, there is an interest in performing statistical inference over these models. A popular methodology for general statistical inference is the bootstrap procedure. Yet, for LFM and FPPE there is no existing theory for the valid application of bootstrap procedures. In this paper, we introduce and devise several statistically valid bootstrap inference procedures for LFM and FPPE. The most challenging part is to bootstrap general FPPE, which reduces to bootstrapping constrained M-estimators, a largely unexplored problem. We devise a bootstrap procedure for FPPE under mild degeneracy conditions by using the powerful tool of epi-convergence theory. Experiments with synthetic and semi-real data verify our theory.

翻译：线性Fisher市场（LFM）是经济学中的基础均衡模型，在公平高效的资源分配中亦有应用。首价调速均衡（FPPE）则刻画了首价拍卖中的预算管理机制。在广告拍卖等实际场景中，常需对这些模型进行统计推断。自举法作为一种通用的统计推断方法广受欢迎，然而针对LFM与FPPE，目前尚缺乏支持自举程序有效应用的理论。本文首次为LFM与FPPE设计并推导了多种统计上有效的自举推断方法。其中最具挑战性的部分是对一般FPPE的自举——该问题可归结为对受限M估计量的自举，而这一领域此前鲜有探索。通过运用epi-收敛理论这一强大工具，我们在温和退化条件下为FPPE构建了自举程序。合成数据与半真实数据的实验验证了我们理论的有效性。