发表机构
Stanford University（斯坦福大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对固定宽度序贯停止机制在无穷方差或长程依赖场景下失效的问题，构建统一框架刻画停止时间与自归一化估计量的渐近行为，提出序贯子抽样过程，在两类场景下得到渐近有效的序贯置信区间并完成验证。
AI 中文摘要
固定宽度序贯停止规则会在随机模拟的估计置信区间达到规定宽度时终止模拟。经典固定宽度理论通常依赖于渐近方差的强一致估计量，这使得归一化停止时间渐近确定，从而可将固定样本量极限理论转移到终止时的估计量上。当模拟输出具有无穷方差或长程依赖时，该机制可能失效。尽管自归一化和子抽样可在固定样本量下产生渐近有效的置信区间，但缩放过程和停止时间可能仍保留非退化随机性，因此固定样本量分位数不一定能在终止时提供有效覆盖率。本文中，我们基于估计过程和缩放过程的联合函数极限定理构建了一个统一框架，刻画了停止时间与终止时自归一化估计量的渐近行为，从而在经典有限方差和无穷方差场景下获得渐近有效的序贯置信区间。此外，我们引入了一种序贯子抽样过程，可在不直接估计极限分布中冗余参数的情况下，一致估计停止时相关的分布。该框架针对重尾移动平均过程、随机近似以及服务时间为重尾的M/G/1排队系统进行了验证。
英文摘要
Fixed-width sequential stopping rules terminate a stochastic simulation once an estimated confidence interval reaches a prescribed width. Classical fixed-width theory typically relies on a strongly consistent estimator of the asymptotic variance. This makes the normalized stopping time asymptotically deterministic, allowing fixed-sample-size limit theory to be transferred to the estimator at termination. This mechanism can fail when simulation output has infinite variance or long-range dependence. Although self-normalization and subsampling can yield asymptotically valid confidence intervals at a fixed sample size, the scaling process and the stopping time may retain nondegenerate randomness, so fixed-sample-size quantiles need not provide valid coverage at termination. In this paper, we develop a unified framework based on a joint functional limit theorem for the estimation process and a scaling process. We characterize the asymptotic behavior of both the stopping time and the self-normalized estimator evaluated at termination, thereby obtaining asymptotically valid sequential confidence intervals in classical finite-variance and infinite-variance settings. Moreover, we introduce a sequential subsampling procedure that consistently estimates the distribution relevant at the stopping time without directly estimating nuisance parameters in the limit distribution. The framework is verified for heavy-tailed moving-average processes, stochastic approximation, and an M/G/1 queue with heavy-tailed service times.
