HIGHER-ORDER COVERAGE ERRORS OF BATCHING METHODS VIA EDGEWORTH EXPANSIONS ON t-STATISTICS

• 成果类型: Article
• 署名作者: He, Shengyi; Lam, Henry
• 署名单位: Columbia University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/24-AOS2377
• 发表日期: 2024
• 页码: 1360-1383
• 关键词: overlapping variance estimators; asymptotic expansions; sequential procedure; OUTPUT ANALYSIS; time-series; functionals; quantiles

摘要

While batching methods have been widely used in simulation and statistics, their higher-order coverage behaviors and relative advantages in this regard remain open. We develop techniques to obtain higher-order coverage errors for batching methods by building Edgeworth-type expansions on t-statistics. The coefficients in these expansions are intricate analytically, but we provide algorithms to estimate the coefficients of the n(-1) error terms via Monte Carlo simulation. We provide insights on the effect of the number of batches on the coverage error, where we demonstrate generally nonmonotonic relations. We also compare different batching methods both theoretically and numerically, and argue that none of the methods is uniformly better than others in terms of coverage. However, when the number of batches is large, sectioned jackknife has the best coverage among all.