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Factorisable Multitask Quantile Regression

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  • Chao, Shih-Kang
  • Härdle, Wolfgang K.
  • Yuan, Ming

Abstract

A multivariate quantile regression model with a factor structure is proposed to study data with multivariate responses with covariates. The factor structure is allowed to vary with the quantile levels, which is more flexible than the classical factor models. Assuming the number of factors is small, and the number of responses and the input variables are growing with the sample size, the model is estimated with the nuclear norm regularization. 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 loss is nonsmooth or the numerical procedure involves expensive subroutines, for example, singular value decomposition. To show that the approximate estimator is still statistically accurate, we establish a nonasymptotic bound on the Frobenius risk and prediction risk. For implementation, a numerical procedure that provably marginalizes the approximation error is proposed. The merits of our model and the proposed numerical procedures are demonstrated through the Monte Carlo simulation and an application to finance involving a large pool of asset returns.

Suggested Citation

  • Chao, Shih-Kang & Härdle, Wolfgang K. & Yuan, Ming, 2021. "Factorisable Multitask Quantile Regression," Econometric Theory, Cambridge University Press, vol. 37(4), pages 794-816, August.
  • Handle: RePEc:cup:etheor:v:37:y:2021:i:4:p:794-816_6
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    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Cuicui Lu & Weining Wang & Jeffrey M. Wooldridge, 2018. "Using generalized estimating equations to estimate nonlinear models with spatial data," Papers 1810.05855, arXiv.org.
    2. Chao, Shih-Kang & Härdle, Wolfgang K. & Huang, Chen, 2018. "Multivariate factorizable expectile regression with application to fMRI data," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 1-19.
    3. Wang, Weining & Wooldridge, Jeffrey M. & Xu, Mengshan, 2020. "Improved Estimation of Dynamic Models of Conditional Means and Variances," IRTG 1792 Discussion Papers 2020-021, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    4. Wang, Weining & Yu, Lining & Wang, Bingling, 2020. "Tail Event Driven Factor Augmented Dynamic Model," IRTG 1792 Discussion Papers 2020-022, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    5. Smith, Lisa C. & Frankenberger, Timothy R., 2022. "Recovering from severe drought in the drylands of Ethiopia: Impact of Comprehensive Resilience Programming," World Development, Elsevier, vol. 156(C).
    6. Perkiss, Stephanie & Bernardi, Cristiana & Dumay, John & Haslam, Jim, 2021. "A sticky chocolate problem: Impression management and counter accounts in the shaping of corporate image," CRITICAL PERSPECTIVES ON ACCOUNTING, Elsevier, vol. 81(C).
    7. Meng, Lina & Zhou, Yinggang & Zhang, Ruige & Ye, Zhen & Xia, Senmao & Cerulli, Giovanni & Casady, Carter & Härdle, Wolfgang Karl, 2020. "The Effect of Control Measures on COVID-19 Transmission and Work Resumption: International Evidence," IRTG 1792 Discussion Papers 2020-011, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".

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    JEL classification:

    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • G20 - Financial Economics - - Financial Institutions and Services - - - General

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