AI 中文总结
研究自举法失效时抽样分布估计问题，提出用神经网络基于弹球损失训练进行摊销推断，该方法在四个典型问题上表现良好，在瓦瑟斯坦距离上优于经典方法，在风险价值问题上也有较好覆盖率，还有单一通用网络匹配多个专门网络的优势。
AI 中文摘要
Efron自举法是估计统计量抽样分布的默认工具，但对于有界支持分布的最大值、无限方差下的均值、极端分位数和尾指数估计量，它被证明是不一致的。经典补救方法，如n中取m自举法和子采样法，需要依赖未知参数的速率校正，并且在实际样本量下行为不稳定。我们提出一种摊销替代方法：在从分布族的先验中抽取的模拟数据集上训练神经网络，使用弹球损失对根\(T_n - T(F)\)的单个独立抽样进行评分，弹球损失是一种适当的评分规则，其总体最小值是根的后验预测律。在测试时，单次前向传递将一个包含\(n = 200\)个观测值的数据集映射到其完整的抽样分布估计，从中可直接得出置信区间。在四个典型的自举法失效问题上，该方法达到名义95%的覆盖率，在与真实抽样分布的瓦瑟斯坦距离上优于所有可行的经典方法，并在可计算精确贝叶斯最优答案的情况下捕获超过97%的可实现改进。对于风险价值问题，没有无分布方法能达到名义覆盖率；学习到的方法达到94.7%。一个带有统计令牌的单一通用网络与所有四个专门网络匹配，在实际每日市场回报上，不变的模型平均覆盖率为0.87，而自举法为0.73，正如我们的族外分析所预测的。
英文摘要
Efron's bootstrap is the default tool for estimating the sampling distribution of a statistic, yet it is provably inconsistent for maxima of bounded-support distributions, means under infinite variance, extreme quantiles, and tail-index estimators. The classical remedies, the m-out-of-n bootstrap and subsampling, require rate corrections that depend on unknown parameters and behave erratically at realistic sample sizes. We propose an amortized alternative: a neural network is trained on simulated datasets drawn from a prior over a distribution family, using single independent draws of the root T_n - T(F) scored by the pinball loss, a proper scoring rule whose population minimizer is the posterior-predictive law of the root. At test time, a single forward pass maps one dataset of n = 200 observations to its full sampling-distribution estimate, from which confidence intervals follow directly. On four canonical bootstrap-failure problems (bounded-support maximum, alpha-stable mean, Pareto tail index, and 99% value-at-risk under tempered stable returns), the method attains nominal 95% coverage, beats every feasible classical method in Wasserstein distance to the true sampling distribution, and captures over 97% of the achievable improvement where the exact Bayes-optimal answer is computable. For the value-at-risk problem no distribution-free method can reach nominal coverage at all; the learned method attains 94.7%. A single universal network with a statistic token matches all four specialists, and on real daily market returns the unchanged model averages 0.87 coverage against 0.73 for the bootstrap, as predicted by our out-of-family analysis.
Comments6 figures, 10 tables. Code and reproducible experiments: https://github.com/akashdeepo/Bootstrap_Backprop
