Adaptive robust confidence intervals
研究Huber污染模型下污染比例未知时如何构造自适应置信区间，发现其最优长度需比非自适应区间呈指数级更宽，且依赖分布形状。适合统计推断研究者参考。
This paper studies the construction of adaptive confidence intervals under Huber’s contamination model when the contamination proportion is unknown. For the robust confidence interval of a Gaussian mean, we show that the optimal length of an adaptive interval must be exponentially wider than that of a nonadaptive one. An optimal construction is achieved through simultaneous uncertainty quantification of quantiles at all levels. The results are further extended beyond the Gaussian location model by addressing a general family of robust hypothesis testing. In contrast to adaptive robust estimation, our findings reveal that the optimal length of an adaptive robust confidence interval critically depends on the distribution’s shape.