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Bootstrap With Cluster‐Dependence in Two or More Dimensions
Author(s) -
Menzel Konrad
Publication year - 2021
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.3982/ecta15383
Subject(s) - consistency (knowledge bases) , mathematics , statistics , asymptotic distribution , cluster analysis , cluster (spacecraft) , inference , sample (material) , uncorrelated , gaussian , regression , computer science , estimator , artificial intelligence , discrete mathematics , physics , quantum mechanics , thermodynamics , programming language
We propose a bootstrap procedure for data that may exhibit cluster‐dependence in two or more dimensions. The asymptotic distribution of the sample mean or other statistics may be non‐Gaussian if observations are dependent but uncorrelated within clusters. We show that there exists no procedure for estimating the limiting distribution of the sample mean under two‐way clustering that achieves uniform consistency. However, we propose bootstrap procedures that achieve adaptivity with respect to different uniformity criteria. Important cases and extensions discussed in the paper include regression inference, U‐ and V‐statistics, subgraph counts for network data, and non‐exhaustive samples of matched data.