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

Yang Chen, Ziyan Luo and Lingchen Kong

Journal of Multivariate Analysis, 2021, vol. 185, issue C

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.

Keywords: Asymptotic properties; Feature selection and estimation; Hellinger risk; ℓ2,0-norm; Multivariate generalized linear models (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.jmva.2021.104782

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