I consider nuclear norm penalized quantile regression for large N and large T  panel data models with interactive fixed effects.  The estimator solves a convex minimization problem, not requiring pre-estimation of the (number of the) fixed effects. Uniform rates are obtained for both the slope coefficients and the low-rank common component of the interactive fixed effects. The rate of the latter is nearly optimal . To derive the rates, I show new results that establish uniform bounds of norms of certain random matrices of jump processes. These results may have independent interest. Finally, I conduct Monte Carlo simulations to illustrate the estimator's finite sample performance .
This paper studies large N and large T conditional quantile panel data models with interactive fixed effects. We propose a nuclear norm penalized estimator of the coefficients on the covariates and the low-rank matrix formed by the fixed effects. The estimator solves a convex minimization problem, not requiring pre-estimation of the (number of the) fixed effects. It also allows the number of covariates to grow slowly with N and T. We derive an error bound on the estimator that holds uniformly in quantile level. The order of the bound implies uniform consistency of the estimator and is nearly optimal for the low-rank component. Given the error bound, we also propose a consistent estimator of the number of fixed effects at any quantile level. To derive the error bound, we develop new theoretical arguments under primitive assumptions and new results on random matrices that may be of independent interest. We demonstrate the performance of the estimator via Monte Carlo simulations .
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I consider nuclear norm penalized quantile regression for
This paper studies
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conditional quantile
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We propose a nuclear norm penalized estimator of the coefficients on the covariates and the low-rank matrix formed by the fixed effects.
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Uniform rates are obtained for both the slope coefficients and the low-rank common component of the interactive fixed effects. The rate of the latter
It also allows the number of covariates to grow slowly with N and T. We derive an error bound on the estimator that holds uniformly in quantile level. The order of the bound implies uniform consistency of the estimator and
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for the low-rank component. Given the error bound, we also propose a consistent estimator of the number of fixed effects at any quantile level.
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rates, I show new results that establish uniform bounds of norms of certain random matrices of jump processes. These results may have
error bound, we develop new theoretical arguments under primitive assumptions and new results on random matrices that may be of
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Finally, I conduct
We demonstrate the performance of the estimator via
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to illustrate the estimator's finite sample performance