Under minimal assumptions, we prove that an empirical estimator of the tail conditional allocation (TCA), also known as the marginal expected shortfall, is consistent. Examples are provided to confirm the minimality of the assumptions. A simulation study illustrates the performance of the estimator in the context of developing confidence intervals for the TCA. The philosophy adopted in the present paper relies on three principles: easiness of practical use, mathematical rigor, and practical justifiability and verifiability of assumptions.

中文翻译：

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最小假设下的经验尾条件分配及其一致性

在最小假设下，我们证明尾部条件分配 (TCA) 的经验估计量（也称为边际预期短缺）是一致的。提供了示例以确认假设的最小性。模拟研究说明了在开发 TCA 置信区间的背景下估计器的性能。本文采用的理念依赖于三个原则：易于实际使用、数学严谨性以及假设的实际合理性和可验证性。