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Asymptotic theory of the adaptive Sparse Group Lasso

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  • Benjamin Poignard

    (Osaka University)

Abstract

We study the asymptotic properties of a new version of the Sparse Group Lasso estimator (SGL), called adaptive SGL. This new version includes two distinct regularization parameters, one for the Lasso penalty and one for the Group Lasso penalty, and we consider the adaptive version of this regularization, where both penalties are weighted by preliminary random coefficients. The asymptotic properties are established in a general framework, where the data are dependent and the loss function is convex. We prove that this estimator satisfies the oracle property: the sparsity-based estimator recovers the true underlying sparse model and is asymptotically normally distributed. We also study its asymptotic properties in a double-asymptotic framework, where the number of parameters diverges with the sample size. We show by simulations and on real data that the adaptive SGL outperforms other oracle-like methods in terms of estimation precision and variable selection.

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  • Benjamin Poignard, 2020. "Asymptotic theory of the adaptive Sparse Group Lasso," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 297-328, February.
    • Handle: RePEc:spr:aistmt:v:72:y:2020:i:1:d:10.1007_s10463-018-0692-7
    DOI: 10.1007/s10463-018-0692-7
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    References listed on IDEAS

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    Cited by:

    1. Xing Qin & Shuangge Ma & Mengyun Wu, 2023. "Two‐level Bayesian interaction analysis for survival data incorporating pathway information," Biometrics, The International Biometric Society, vol. 79(3), pages 1761-1774, September.
    2. Kaida Cai & Hua Shen & Xuewen Lu, 2022. "Adaptive bi-level variable selection for multivariate failure time model with a diverging number of covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 968-993, December.
    3. Benjamin Poignard & Manabu Asai, 2023. "High‐dimensional sparse multivariate stochastic volatility models," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(1), pages 4-22, January.

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