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Factorisable Multitask Quantile Regression

Shih-Kang Chao, Wolfgang Härdle () and Ming Yuan

No 2020-004, IRTG 1792 Discussion Papers from Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series"

Abstract: A multivariate quantile regression model with a factor structure is proposed to study data with many responses of interest. The factor structure is allowed to vary with the quantile levels, which makes our framework more flexible than the classical factor models. The model is estimated with the nuclear norm regularization in order to accommodate the high dimensionality of data, but the incurred optimization problem can only be efficiently solved in an approximate manner by off-the-shelf optimization methods. Such a scenario is often seen when the empirical risk is non-smooth or the numerical procedure involves expensive subroutines such as singular value decompo- sition. To ensure that the approximate estimator accurately estimates the model, non-asymptotic bounds on error of the the approximate estimator is established. For implementation, a numerical procedure that provably marginalizes the approximate error is proposed. The merits of our model and the proposed numerical procedures are demonstrated through Monte Carlo experiments and an application to finance involving a large pool of asset returns.

Keywords: Factor model; quantile regression; non-asymptotic analysis; multivariate regression; nuclear norm regularization (search for similar items in EconPapers)
JEL-codes: C13 C38 C61 G17 (search for similar items in EconPapers)
Date: 2020
New Economics Papers: this item is included in nep-ecm and nep-ore
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Related works:
Journal Article: FACTORISABLE MULTITASK QUANTILE REGRESSION (2021) Downloads
Working Paper: Factorisable Multi-Task Quantile Regression (2016) Downloads
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