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Canonical correlation regression with noisy data

Isaac Meza, Rahul Singh

arXiv 27 Dec 2025 · Econometrics

arXiv:2512.22697 · PDF · DOI · OpenAlex · Extracted main text

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.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Bao, Z., Hu, J., Pan, G., and Zhou, W (2019) Canonical correlation coefficients of high-dimensional gaussian vectors: Finite rank case0.64422100%
2Benaych-Georges, F. and Nadakuditi, R. R (2012) The singular values and vectors of low rank perturbations of large rectangular random matrices0.64422100%
3Andrews, I (2016) Conditional linear combination tests for weakly identified models0.40511100%
4Andrews, I (2018) Valid two-step identification-robust confidence sets for GMM0.40511100%
5Bai, J. and Ng, S (2006) Confidence intervals for diffusion index forecasts and inference for factor-augmented regressions0.40511100%
6Bai, J. and Ng, S (2010) Instrumental variable estimation in a data rich environment0.40511100%
7Bai, J. and Wang, P (2016) Econometric analysis of large factor models0.40511100%
8Baik, J., Ben Arous, G., and Péché, S (2005) Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices0.40511100%
9Carrasco, M (2012) A regularization approach to the many instruments problem0.40511100%
10Carrasco, M. and Tchuente, G (2016) Regularization based Anderson–Rubin tests for many instruments0.40511100%

Showing the top 10 of 36 scored citations.