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Title: High dimensional latent quantile regression Authors:  Oscar Hernan Padilla - UCLA (United States) [presenting]
Abstract: A novel estimator is proposed for high dimensional latent quantile regression. The approach consists in combining the quantile loss function with recent advances in convex optimization. The resulting estimator can naturally be used for applications where there is interest in variable selection in high dimensions (perhaps $p$ larger than $n$), but in the presence of low-rank latent factors. On the theoretical side, we consider a setting that allows for lagged dependency and show that, under suitable regularity conditions, for a fixed quantile level, our estimator can consistently estimate both, the vector of coefficients and the latent factor matrix. On the computationally side, we provide a solution algorithm based on the popular alternating method of multipliers. Finally, our experiments in real data show the value of our proposed method for interpretation of the latent factors, and variable selection.