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ℓ2,0-norm based selection and estimation for multivariate generalized linear models

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  • Chen, Yang
  • Luo, Ziyan
  • Kong, Lingchen

Abstract

Group sparse regression has been well considered in multivariate linear models with appropriate relaxation schemes for the involved ℓ2,0-norm penalty. Lacking of the extended research on multivariate generalized linear models (GLMs), this paper targets at the original discontinuous and nonconvex ℓ2,0-norm based selection and estimation for multivariate GLMs. Under mild conditions, we give a necessary condition for selection consistency based on the notion of degree of separation, and propose the feature selection consistency as well as optimal coefficient estimation for the resulting ℓ2,0-likelihood estimators in terms of the Hellinger risk. Numerical studies on synthetic data and a real data in chemometrics confirm superior performance of the ℓ2,0-likelihood methods.

Suggested Citation

  • Chen, Yang & Luo, Ziyan & Kong, Lingchen, 2021. "ℓ2,0-norm based selection and estimation for multivariate generalized linear models," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    • Handle: RePEc:eee:jmvana:v:185:y:2021:i:c:s0047259x21000609
    DOI: 10.1016/j.jmva.2021.104782
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    References listed on IDEAS

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