Square-root nuclear norm penalized estimator for panel data models with approximately low-rank unobserved heterogeneity

2019/04/19 by Jad Beyhum, Beyhum, Jad, Éric Gautier +1 · 2 citations
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Spatial and Panel Data Analysis #Statistical Methods and Inference #Statistical and numerical algorithms #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1904.09192

openalex publication_date 2019/04/19 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

This paper considers a nuclear norm penalized estimator for panel data models with interactive effects. The low-rank interactive effects can be an approximate model and the rank of the best approximation unknown and grow with sample size. The estimator is solution of a well-structured convex optimization problem and can be solved in polynomial-time. We derive rates of convergence, study the low-rank properties of the estimator, estimation of the rank and of annihilator matrices when the number of time periods grows with the sample size. Two-stage estimators can be asymptotically normal. None of the procedures require knowledge of the variance of the errors.

Cited by

• Regularized Quantile Regression with Interactive Fixed Effects
• Inference on panel data models with a generalized factor structure

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