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Doubly Robust Inference in Causal Latent Factor Models (2402.11652v3)
Published 18 Feb 2024 in econ.EM, cs.LG, stat.ME, and stat.ML
Abstract: This article introduces a new estimator of average treatment effects under unobserved confounding in modern data-rich environments featuring large numbers of units and outcomes. The proposed estimator is doubly robust, combining outcome imputation, inverse probability weighting, and a novel cross-fitting procedure for matrix completion. We derive finite-sample and asymptotic guarantees, and show that the error of the new estimator converges to a mean-zero Gaussian distribution at a parametric rate. Simulation results demonstrate the relevance of the formal properties of the estimators analyzed in this article.
- Synthetic control methods for comparative case studies: Estimating the effect of california’s tobacco control program. Journal of the American Statistical Association, 105(490):493–505.
- Large sample properties of matching estimators for average treatment effects. Econometrica, 74(1):235–267.
- Causal matrix completion. In The Thirty Sixth Annual Conference on Learning Theory, pages 3821–3826. PMLR.
- Synthetic interventions.
- On robustness of principal component regression. Journal of the American Statistical Association, pages 1–34.
- Angrist, J. D. (1998). Estimating the labor market impact of voluntary military service using social security data on military applicants. Econometrica, 66(2):249–288.
- Synthetic difference-in-differences. American Economic Review, 111(12):4088–4118.
- Matrix completion methods for causal panel data models. Journal of the American Statistical Association, 116(536):1716–1730.
- Bai, J. (2003). Inferential theory for factor models of large dimensions. Econometrica, 71(1):135–171.
- Bai, J. (2009). Panel data models with interactive fixed effects. Econometrica, 77(4):1229–1279.
- Determining the number of factors in approximate factor models. Econometrica, 70(1):191–221.
- Matrix completion, counterfactuals, and factor analysis of missing data. Journal of the American Statistical Association, 116(536):1746–1763.
- Doubly robust estimation in missing data and causal inference models. Biometrics, 61(4):962–972.
- Bhatia, R. (2007). Perturbation bounds for matrix eigenvalues. SIAM.
- Matrix completion with data-dependent missingness probabilities. IEEE Transactions on Information Theory, 68(10):6762–6773.
- Billingsley, P. (2017). Probability and measure. John Wiley & Sons.
- Chatterjee, S. (2015). Matrix estimation by universal singular value thresholding. The Annals of Statistics, 43(1):177 – 214.
- Double/debiased machine learning for treatment and structural parameters. The Econometrics Journal, 21(1):C1–C68.
- Cochran, W. G. (1968). The effectiveness of adjustment by subclassification in removing bias in observational studies. Biometrics, pages 295–313.
- Counterfactual inference for sequential experiments. arXiv preprint arXiv:2202.06891.
- Doubly robust nearest neighbors in factor models. arXiv preprint arXiv:2211.14297.
- Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction. Cambridge University Press.
- Nearest neighbors for matrix estimation interpreted as blind regression for latent variable model. IEEE Transactions on Information Theory, 66(3):1760–1784.
- Missing not at random in matrix completion: The effectiveness of estimating missingness probabilities under a low nuclear norm assumption. Advances in neural information processing systems, 32.
- Low-rank matrix completion: A contemporary survey. IEEE Access, 7:94215–94237.
- The central role of the propensity score in observational studies for causal effects. Biometrika, 70(1):41–55.
- Tropp, J. A. (2012). User-friendly tail bounds for sums of random matrices. Foundations of computational mathematics, 12:389–434.
- Vershynin, R. (2018). High-dimensional probability: An introduction with applications in data science, volume 47. Cambridge university press.