Learning Centre Partitions from Summaries

• URL: http://arxiv.org/abs/2509.16337v1
• Date: Fri, 19 Sep 2025 18:25:06 GMT
• Title: Learning Centre Partitions from Summaries
• Authors: Zinsou Max Debaly, Jean-Francois Ethier, Michael H. Neumann, Félix Camirand Lemyre,
• Abstract summary: Homogeneity of parameters across centres is often violated, motivating methods that both emphtest for equality and emphlearn centre groupings before estimation.<n>We develop a sequential, test-driven emphClusters-of-Centres (CoC) algorithm that merges centres (or blocks) only when equality is not rejected.
• Score: 0.21748200848556343
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 \emph{test} for equality and \emph{learn} centre groupings before estimation. We develop multivariate Cochran-type tests that operate on summary statistics and embed them in a sequential, test-driven \emph{Clusters-of-Centres (CoC)} algorithm that merges centres (or blocks) only when equality is not rejected. We derive the asymptotic $\chi^2$-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 \emph{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.

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