Regression of exchangeable relational arrays

Summary Relational arrays represent measures of association between pairs actors, often in varied contexts or over time. Trade flows countries, financial transactions individuals, contact frequencies school children classrooms and dynamic protein-protein interactions are all examples relational arrays. Elements a array modelled as linear function observable covariates. Uncertainty estimates for regression coefficient estimators, ideally the estimators themselves, must account dependence elements array, e.g., relations involving same actor. Existing standard errors that recognize such rely on estimating extremely complex, heterogeneous structure across actors. This paper develops new class parsimonious error regressions We leverage an exchangeability assumption to derive pool information substantially more accurate than existing variety settings. is pervasive network models statistics literature, but not previously considered when adjusting setting with data. demonstrate improvements inference theoretically, via simulation study, by analysis dataset international trade.