Quantifying Distributional Model Risk in Marginal Problems via Optimal Transport

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Tác giả: Yanqin Fan, Hyeonseok Park, Gaoqian Xu

Ngôn ngữ: eng

Ký hiệu phân loại: 003.78 Distributed-parameter systems

Thông tin xuất bản: 2023

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Bộ sưu tập: Metadata

ID: 197621

 This paper studies distributional model risk in marginal problems, where each marginal measure is assumed to lie in a Wasserstein ball centered at a fixed reference measure with a given radius. Theoretically, we establish several fundamental results including strong duality, finiteness of the proposed Wasserstein distributional model risk, and the existence of an optimizer at each radius. In addition, we show continuity of the Wasserstein distributional model risk as a function of the radius. Using strong duality, we extend the well-known Makarov bounds for the distribution function of the sum of two random variables with given marginals to Wasserstein distributionally robust Markarov bounds. Practically, we illustrate our results on four distinct applications when the sample information comes from multiple data sources and only some marginal reference measures are identified. They are: partial identification of treatment effects
  externally valid treatment choice via robust welfare functions
  Wasserstein distributionally robust estimation under data combination
  and evaluation of the worst aggregate risk measures.
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