Simultaneous estimation and variable selection for a non-crossing multiple quantile regression using deep neural networks

Jungmin Shin, Seunghyun Gwak, Seung Jun Shin, Sungwan Bang

Research output: Contribution to journalArticlepeer-review


In this paper, we present the DNN-NMQR estimator, an approach that utilizes a deep neural network structure to solve multiple quantile regression problems. When estimating multiple quantiles, our approach leverages the structural characteristics of DNN to enhance estimation results by encouraging shared learning across different quantiles through DNN-NMQR. Also, this method effectively addresses quantile crossing issues through the penalization method. To refine our methodology, we introduce a convolution-type quadratic smoothing function, ensuring that the objective function remains differentiable throughout. Furthermore, we provide a brief discussion on the convergence analysis of DNN-NMQR, drawing on the concept of the neural tangent kernel. For a high-dimensional case, we propose the (A)GDNN-NMQR estimator, which applies group-wise L1-type regularization methods and enjoys the advantages of quantile estimation and variable selection simultaneously. We extensively validate all of our proposed methods through numerical experiments and real data analysis.

Original languageEnglish
Article number102
JournalStatistics and Computing
Issue number3
Publication statusPublished - 2024 Jun

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.


  • Deep neural network
  • Multiple quantile regression
  • Neural tangent kernel
  • Non-crossing
  • Smoothing function
  • Variable selection

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computational Theory and Mathematics


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