2020/09/14 by Qiaohui Lin, Lin, Qiaohui, Robert Lunde +3 · 1 citation
Computer Science · Mathematics · #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Methodology (stat.ME) #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2009.06170
openalex publication_date 2020/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a new class of multiplier bootstraps for count functionals, ranging from a fast, approximate linear bootstrap tailored to sparse, massive graphs to a quadratic bootstrap procedure that offers refined accuracy for smaller, denser graphs. For the fast, approximate linear bootstrap, we show that √(n)-consistent inference of the count functional is attainable in certain computational regimes that depend on the sparsity level of the graph. Furthermore, even in more challenging regimes, we prove that our bootstrap procedure offers valid coverage and vanishing confidence intervals. For the quadratic bootstrap, we establish an Edgeworth expansion and show that this procedure offers higher-order accuracy under appropriate sparsity conditions. We complement our theoretical results with a simulation study and real data analysis and verify that our procedure offers state-of-the-art performance for several functionals.