Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/162499
Authors: 
Chao, Shih-Kang
Härdle, Wolfgang
Yuan, Ming
Year of Publication: 
2016
Series/Report no.: 
SFB 649 Discussion Paper 2016-057
Abstract: 
For many applications, analyzing multiple response variables jointly is desirable because of their dependency, and valuable information about the distribution can be retrieved by estimating quantiles. In this paper, we propose a multi-task quantile regression method that exploits the potential factor structure of multivariate conditional quantiles through nuclear norm regularization. We jointly study the theoretical properties and computational aspects of the estimating procedure. In particular, we develop an efficient iterative proximal gradient algorithm for the non-smooth and non-strictly convex optimization problem incurred in our estimating procedure, and derive oracle bounds for the estimation error in a realistic situation where the sample size and number of iterative steps are both finite. The finite iteration analysis is particular useful when the matrix to be estimated is big and the computational cost is high. Merits of the proposed methodology are demonstrated through a Monte Carlo experiment and applications to climatological and financial study. Specifically, our method provides an objective foundation for spatial extreme clustering, and gives a refreshing look on the global financial systemic risk. Supplementary materials for this article are available online.
Subjects: 
Factor model
Fast iterative shrinkage-thresholding algorithm
Multivariate regression
Spatial extreme
Financial risk
Document Type: 
Working Paper
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