外推感知的非参数统计推断
Extrapolation-Aware Nonparametric Statistical Inference
AI总结：
本文扩展非参数统计模型，提出基于观测支撑集内方向导数极值的外推假设与一致界估计方法，用于预测和不确定性量化。
摘要：
我们将外推定义为：对在条件变量支撑集之外取值的条件函数（例如条件期望或条件分位数）进行的任何类型的统计推断。这类外推出现在许多数据分析应用中，如果不加以考虑，可能会使所得结论失效。虽然外推在参数模型中很直接，但在非参数模型中却具有挑战性。在本工作中，我们扩展了非参数统计模型，以明确允许外推，并引入一类外推假设；这些假设可与现有推断技术结合，得出外推感知的结论。所提出的这类外推假设规定，在每个方向上，条件函数都在观测支撑集内取得其最小和最大方向导数。我们说明了该框架如何应用于若干统计应用，包括预测和不确定性量化。此外，我们提出了一种一致估计程序，可通过提供下外推界和上外推界来调整现有非参数估计，以考虑外推。该程序在模拟数据和真实世界数据上都进行了实证评估。
英文摘要：
We define extrapolation as any type of statistical inference on a conditional function (e.g., a conditional expectation or conditional quantile) evaluated outside of the support of the conditioning variable. This type of extrapolation occurs in many data analysis applications and can invalidate the resulting conclusions if not taken into account. While extrapolating is straightforward in parametric models, it becomes challenging in nonparametric models. In this work, we extend the nonparametric statistical model to explicitly allow for extrapolation and introduce a class of extrapolation assumptions that can be combined with existing inference techniques to draw extrapolation-aware conclusions. The proposed class of extrapolation assumptions stipulate that the conditional function attains its minimal and maximal directional derivative, in each direction, within the observed support. We illustrate how the framework applies to several statistical applications including prediction and uncertainty quantification. We furthermore propose a consistent estimation procedure that can be used to adjust existing nonparametric estimates to account for extrapolation by providing lower and upper extrapolation bounds. The procedure is empirically evaluated on both simulated and real-world data.
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