Accounting for both rare events and complex sampling presents challenges when quantifying uncertainty for rate estimation in autonomous vehicle performance evaluation. In this paper, we introduce a statistical formulation of this problem and develop a unified compound Poisson model framework for unbiased rate estimation through the Horvitz Thompson estimator. Though asymptotic theory for the model is available, the inference of confidence intervals (CIs) in the presence of rare events requires new investigation. We also advocate for a new monotonicity criterion for rate CIs--summing the rates of disjoint types of events should produce not only a higher point estimate but also higher confidence bounds than for the individual rates--that facilitates interpretability in real applications. We propose a novel exponential bootstrap (EB) method for CI construction based on a fiducial argument; it satisfies the monotonicity property, while novel extensions of some existing methods do not. Comprehensive numerical studies show that EB performs well for a wide range of settings relevant to our applications. Fast implementation of EB based on saddlepoint approximation is also developed, which may be of independent interest.

翻译：针对自动驾驶性能评估中的率估计，在量化不确定性时，处理罕见事件与复杂采样同时存在的情况具有挑战性。本文提出了该问题的统计框架，并建立了基于霍维茨-汤普森估计量的无偏率估计统一复合泊松模型。尽管该模型已有渐近理论可用，但罕见事件存在时置信区间的推断仍需新的研究。我们主张为率置信区间提出一种新的单调性准则——不同不相交事件类型率的加和不仅应产生比单个率更高的点估计，还应产生更高的置信界——这有利于实际应用中的可解释性。我们基于信任论证提出了新颖的指数自助法用于置信区间构建；该方法满足单调性，而现有方法的新扩展则不然。广泛的数值研究表明，在大量与我们应用相关的设定中，指数自助法表现良好。我们还基于鞍点逼近开发了指数自助法的快速实现，这本身可能具有独立的研究价值。