{"ID":2824884,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.22697","arxiv_id":"2512.22697","title":"Canonical correlation regression with noisy data","abstract":"We study instrumental variable regression in data rich environments. The goal is to estimate a linear model from many noisy covariates and many noisy instruments. Our key assumption is that true covariates and true instruments are repetitive, though possibly different in nature; they each reflect a few underlying factors, however those underlying factors may be misaligned. We analyze a family of estimators based on two stage least squares with spectral regularization: canonical correlations between covariates and instruments are learned in the first stage, which are used as regressors in the second stage. As a theoretical contribution, we derive upper and lower bounds on estimation error, proving optimality of the method with noisy data. As a practical contribution, we provide guidance on which types of spectral regularization to use in different regimes.","short_abstract":"We study instrumental variable regression in data rich environments. The goal is to estimate a linear model from many noisy covariates and many noisy instruments. Our key assumption is that true covariates and true instruments are repetitive, though possibly different in nature; they each reflect a few underlying facto...","url_abs":"https://arxiv.org/abs/2512.22697","url_pdf":"https://arxiv.org/pdf/2512.22697v1","authors":"[\"Isaac Meza\",\"Rahul Singh\"]","published":"2025-12-27T20:08:15Z","proceeding":"econ.EM","tasks":"[\"econ.EM\",\"math.ST\",\"stat.ML\"]","methods":"[]","has_code":false}