Learning Centre Partitions from Summaries

Multi-centre studies increasingly rely on distributed inference, where sites share only centre-level summaries. Homogeneity of parameters across centres is often violated, motivating methods that both test for equality and learn centre groupings before estimation. We develop multivariate Cochran-type tests that operate on summary statistics and embed them in a sequential, test-driven Clusters-of-Centres (CoC) algorithm that merges centres (or blocks) only when equality is not rejected. We derive the asymptotic chi2-mixture distributions of the test statistics and provide plug-in estimators for implementation. To improve finite-sample integration, we introduce a multi-round bootstrap CoC that re-evaluates merges across independently resampled summary sets; under mild regularity and a separation condition, we prove a golden-partition recovery result: as the number of rounds grows with n, the true partition is recovered with probability tending to one. We also give simple numerical guidelines, including a plateau-based stopping rule, to make the multi-round procedure reproducible. Simulations and a real-data analysis of U.S. airline on-time performance (2007) show accurate heterogeneity detection and partitions that change little with the choice of resampling scheme.