We propose a high dimensional mean test framework for shrinking random variables, where the underlying random variables shrink to zero as the sample size increases. By pooling observations across overlapping subsets of dimensions, we estimate subsets means and test whether the maximum absolute mean deviates from zero. This approach overcomes cancellations that occur in simple averaging and remains valid even when marginal asymptotic normality fails. We establish theoretical properties of the test statistic and develop a multiplier bootstrap procedure to approximate its distribution. The method provides a flexible and powerful tool for the validation and comparative backtesting of value-at-risk. Simulations show superior performance in high-dimensional settings, and a real-data application demonstrates its practical effectiveness in backtesting.

翻译：本文提出了一种针对收缩随机变量的高维均值检验框架，其中基础随机变量随样本量增加而收缩至零。通过汇集跨维度重叠子集的观测值，我们估计子集均值并检验最大绝对均值是否偏离零。该方法克服了简单平均中出现的抵消效应，即使在边缘渐近正态性失效时仍保持有效性。我们建立了检验统计量的理论性质，并开发了乘数自助法来近似其分布。该方法为风险价值的验证与比较回测提供了灵活而强大的工具。模拟实验表明其在高压维场景下的优越性能，实际数据应用则验证了其在回测中的实践有效性。