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Recovery of partly sparse and dense signals

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  • Miyazaki, Izuru

Abstract

In high-dimensional data analysis, we often encounter partly sparse and dense signals or parameters. Considering an lq-penalization with different qs for each sub-vector of the signals, we formularize an optimal solution for q=1 or 2 in a linear regression model to well represent such signals or parameters. We also provide an algorithm to derive it. Furthermore, we provide the consistency result of the variable selection in this optimal solution under a fixed design. Simulation study and real-data analysis illustrate its improved variable selection performance relative to the conventional methods.

Suggested Citation

  • Miyazaki, Izuru, 2023. "Recovery of partly sparse and dense signals," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    • Handle: RePEc:eee:jmvana:v:195:y:2023:i:c:s0047259x23000076
    DOI: 10.1016/j.jmva.2023.105161
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    References listed on IDEAS

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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Ferraty, F., 2010. "High-dimensional data: a fascinating statistical challenge," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 305-306, February.
    3. Harrar, Solomon W. & Kong, Xiaoli, 2022. "Recent developments in high-dimensional inference for multivariate data: Parametric, semiparametric and nonparametric approaches," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    4. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    5. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    6. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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