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Group penalized expectile regression

Author

Listed:
  • Mohamed Ouhourane

    (Université du Québec à Montréal)

  • Karim Oualkacha

    (Université du Québec à Montréal)

  • Archer Yi Yang

    (McGill University)

Abstract

The asymmetric least squares regression (or expectile regression) allows estimating unknown expectiles of the conditional distribution of a response variable as a function of a set of predictors and can handle heteroscedasticity issues. High dimensional data, such as omics data, are error prone and usually display heterogeneity. Such heterogeneity is often of scientific interest. In this work, we propose the Group Penalized Expectile Regression (GPER) approach, under high dimensional settings. GPER considers implementation of sparse expectile regression with group Lasso penalty and the group non-convex penalties. However, GPER may fail to tell which groups variables are important for the conditional mean and which groups of variables are important for the conditional scale/variance. To that end, we further propose a COupled Group Penalized Expectile Regression (COGPER) regression which can be efficiently solved by an algorithm similar to that for solving GPER. We establish theoretical properties of the proposed approaches. In particular, GPER and COGPER using the SCAD penalty or MCP is shown to consistently identify the two important subsets for the mean and scale simultaneously. We demonstrate the empirical performance of GPER and COGPER by simulated and real data.

Suggested Citation

  • Mohamed Ouhourane & Karim Oualkacha & Archer Yi Yang, 2024. "Group penalized expectile regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 33(5), pages 1251-1313, November.
    • Handle: RePEc:spr:stmapp:v:33:y:2024:i:5:d:10.1007_s10260-024-00768-8
    DOI: 10.1007/s10260-024-00768-8
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    References listed on IDEAS

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    9. Lina Liao & Cheolwoo Park & Hosik Choi, 2019. "Penalized expectile regression: an alternative to penalized quantile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(2), pages 409-438, April.
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