Learning Centre Partitions from Summaries
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914372493770752 |
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| author | Debaly, Zinsou Max Ethier, Jean-Francois Neumann, Michael H. Camirand-Lemyre, Félix |
| author_facet | Debaly, Zinsou Max Ethier, Jean-Francois Neumann, Michael H. Camirand-Lemyre, Félix |
| contents | 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 $χ^2$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16337 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning Centre Partitions from Summaries Debaly, Zinsou Max Ethier, Jean-Francois Neumann, Michael H. Camirand-Lemyre, Félix Methodology Statistics Theory Applications Machine Learning 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 $χ^2$-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. |
| title | Learning Centre Partitions from Summaries |
| topic | Methodology Statistics Theory Applications Machine Learning |
| url | https://arxiv.org/abs/2509.16337 |