Factorisable Multitask Quantile Regression

65 Pages Posted: 8 Feb 2020 Last revised: 29 Jul 2020

See all articles by Shih-Kang Chao

Shih-Kang Chao

University of Missouri - Columbia

Wolfgang K. Härdle

Humboldt University of Berlin - Institute for Statistics and Econometrics; Xiamen University - Wang Yanan Institute for Studies in Economics (WISE); Charles University; Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Ming Yuan

Columbia University

Date Written: January 17, 2020

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

JEL Classification: C13, C38, C61, G17

Suggested Citation

Chao, Shih-Kang and Härdle, Wolfgang K. and Yuan, Ming, Factorisable Multitask Quantile Regression (January 17, 2020). Available at SSRN: https://ssrn.com/abstract=3521887 or http://dx.doi.org/10.2139/ssrn.3521887

Shih-Kang Chao (Contact Author)

University of Missouri - Columbia ( email )

Columbia, MO 65203
United States

Wolfgang K. Härdle

Humboldt University of Berlin - Institute for Statistics and Econometrics ( email )

Unter den Linden 6
Berlin, D-10099
Germany

Xiamen University - Wang Yanan Institute for Studies in Economics (WISE) ( email )

A 307, Economics Building
Xiamen, Fujian 10246
China

Charles University ( email )

Celetná 13
Dept Math Physics
Praha 1, 116 36
Czech Republic

Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Unter den Linden 6
Berlin, D-10099
Germany

Ming Yuan

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

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