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High-dimensional nonconvex LASSO-type M-estimators

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  • Beyhum, Jad
  • Portier, François

Abstract

A theory is developed to examine the convergence properties of ℓ1-norm penalized high-dimensional M-estimators, with nonconvex risk and unrestricted domain. Under high-level conditions, the estimators are shown to attain the rate of convergence s0log(nd)/n, where s0 is the number of nonzero coefficients of the parameter of interest. Sufficient conditions for our main assumptions are then developed and finally used in several examples including robust linear regression, binary classification and nonlinear least squares.

Suggested Citation

  • Beyhum, Jad & Portier, François, 2024. "High-dimensional nonconvex LASSO-type M-estimators," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    • Handle: RePEc:eee:jmvana:v:202:y:2024:i:c:s0047259x24000101
    DOI: 10.1016/j.jmva.2024.105303
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    References listed on IDEAS

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    1. Wang, Lan & Kai, Bo & Heuchenne, Cedric & Tsai, Chih- Ling, 2013. "Penalized profiled semiparametric estimating functions," LIDAM Reprints ISBA 2013042, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Lukas Meier & Sara Van De Geer & Peter Bühlmann, 2008. "The group lasso for logistic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 53-71, February.
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