2021/11/12 by Shengyi He, He, Shengyi, Henry Lam +1 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Probability (math.PR) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2111.06859
openalex publication_date 2021/11/12 · openalex created_date 2021/11/22 · openalex updated_date 2026/07/28
While batching methods have been widely used in simulation and statistics, it is open regarding their higher-order coverage behaviors and whether one variant is better than the others in this regard. 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 term via Monte Carlo simulation. We provide insights on the effect of the number of batches on the coverage error where we demonstrate generally non-monotonic relations. We also compare different batching methods both theoretically and numerically, and argue that none of the methods is uniformly better than the others in terms of coverage. However, when the number of batches is large, sectioned jackknife has the best coverage among all.