Multivariate Factorisable Sparse Asymmetric Least Squares Regression

SFB 649 Discussion Paper 2016-058

32 Pages Posted: 29 Dec 2016

See all articles by Shih-Kang Chao

Shih-Kang Chao

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

Wolfgang K. Härdle

Blockchain Research Center; Xiamen University - Wang Yanan Institute for Studies in Economics (WISE); Charles University; National Yang Ming Chiao Tung University; Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Chen Huang

Aarhus University - Department of Economics and Business Economics

Date Written: December 23, 2016

Abstract

More and more data are observed in form of curves. Numerous applications in finance, neuroeconomics, demographics and also weather and climate analysis make it necessary to extract common patterns and prompt joint modelling of individual curve variation. Focus of such joint variation analysis has been on fluctuations around a mean curve, a statistical task that can be solved via functional PCA. In a variety of questions concerning the above applications one is more interested in the tail asking therefore for tail event curves (TEC) studies. With increasing dimension of curves and complexity of the covariates though one faces numerical problems and has to look into sparsity related issues. Here the idea of Factorisable Sparse Tail Event Curves (FASTEC) via multivariate asymmetric least squares regression (expectile regression) in a high-dimensional framework is proposed. Expectile regression captures the tail moments globally and the smooth loss function improves the convergence rate in the iterative estimation algorithm compared with quantile regression. The necessary penalization is done via the nuclear norm. Finite sample oracle properties of the estimator associated with asymmetric squared error loss and nuclear norm regularizer are studied formally in this paper. As an empirical illustration, the FASTEC technique is applied on fMRI data to see if individual’s risk perception can be recovered by brain activities. Results show that factor loadings over different tail levels can be employed to predict individual’s risk attitudes.

Keywords: high-dimensional M-estimator, nuclear norm regularizer, factorization, expectile regression, fMRI, risk perception, multivariate functional data

JEL Classification: C38, C55, C61, C91, D87

Suggested Citation

Chao, Shih-Kang and Härdle, Wolfgang K. and Huang, Chen, Multivariate Factorisable Sparse Asymmetric Least Squares Regression (December 23, 2016). SFB 649 Discussion Paper 2016-058, Available at SSRN: https://ssrn.com/abstract=2891279

Shih-Kang Chao

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

Spandauer Strasse 1
Berlin, D-10178
Germany

Wolfgang K. Härdle (Contact Author)

Blockchain Research Center ( 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

National Yang Ming Chiao Tung University ( email )

No. 1001, Daxue Rd. East Dist.
Hsinchu City 300093
Taiwan

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

Unter den Linden 6
Berlin, D-10099
Germany

Chen Huang

Aarhus University - Department of Economics and Business Economics ( email )

Fuglesangs Allé 4
Aarhus V, 8210
Denmark

Do you want regular updates from SSRN on Twitter?

Paper statistics

Downloads
54
Abstract Views
413
rank
497,590
PlumX Metrics