Canonical Correlation Regression with Noisy Data

This paper addresses the problem of estimating linear models in data-rich environments with noisy covariates and instruments, a common challenge in fields like econometrics and causal inference. The core contribution lies in proposing and analyzing an estimator based on canonical correlation analysis (CCA) and spectral regularization. The theoretical analysis, including upper and lower bounds on estimation error, is significant as it provides guarantees on the method's performance. The practical guidance on regularization techniques is also valuable for practitioners.

• •Proposes a CCA-based estimator for instrumental variable regression with noisy data.
• •Provides theoretical guarantees (upper and lower bounds) on the estimator's performance.
• •Offers practical guidance on spectral regularization techniques.
• •Addresses a relevant problem in data-rich environments.