Sequential Bootstrap for Out-of-Bag Error Estimation: A 100-Seed Replication Study and Variance-Structure Analysis

Statistics > Methodology [Submitted on 22 Nov 2025 (v1), last revised 1 Jun 2026 (this version, v2)] Title:Sequential Bootstrap for Out-of-Bag Error Estimation: A 100-Seed Replication Study and Variance-Structure Analysis View PDFAbstract:Out-of-Bag (OOB) estimation is the standard internal diagnostic for bootstrap-aggregated tree ensembles. Under the classical multinomial bootstrap, the number of distinct training observations in each replicate, $U_b$, is itself random, but its contribution to OOB-based variability has rarely been isolated empirically. We use Sequential Bootstrap (SB) -- a resampling scheme that holds $U_b$ at a fixed target $k_n = \lfloor 0.632 n\rfloor$ -- as a controlled perturbation of the bootstrap mechanism, and ask whether stabilizing $U_b$ produces any measurable change in OOB-based diagnostics. We reproduce Breiman's five OOB experimental families on twelve synthetic and real datasets, but unlike the three-seed presentation common in this literature, we run 100 independent random seeds with 50 internal replications per seed, enabling formal paired statistical comparison (Wilcoxon signed-rank, paired-$t$, Pitman--Morgan variance test). We report three findings. First, OOB means are essentially insensitive to stabilization of $U_b$: of 57 (experiment, dataset, metric) cells under 100 seeds, only 6 reach $p<0.05$ on the paired mean comparison, and 4 of those 6 point in the opposite direction from what a 3-seed reading would suggest. Second, a narrow but reproducible effect survives at the variance level: SB reduces the cross-seed standard deviation of node-level classification diagnostics on real datasets while slightly increasing it on synthetic ones (permutation $p=0.026$); the Vehicle dataset exhibits a 21% cross-seed sd reduction (Pitman--Morgan $p=0.017$). Third, several directional claims that appear stable across three seeds flip sign under 100-seed replication, illustrating the cost of underpowered replication protocols. We therefore treat SB as a diagnostic tool for probing the distinct-sample-count term in the variance of OOB estimators, not as an alternative to the classical bootstrap. Submission history From: Cheng Peng [view email][v1] Sat, 22 Nov 2025 13:56:50 UTC (113 KB) [v2] Mon, 1 Jun 2026 06:15:20 UTC (133 KB) References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.