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Optimal designs in sparse linear models

Author

Listed:
  • Yimin Huang

    (Peking University)

  • Xiangshun Kong

    (Beijing Institute of Technology)

  • Mingyao Ai

    (Peking University)

Abstract

The Lasso approach is widely adopted for screening and estimating active effects in sparse linear models with quantitative factors. Many design schemes have been proposed based on different criteria to make the Lasso estimator more accurate. This article applies $$\varPhi _l$$Φl-optimality to the asymptotic covariance matrix of the Lasso estimator. Smaller mean squared error and higher power of significant hypothesis tests can be achieved. A theoretically converging algorithm is given for searching for $$\varPhi _l$$Φl-optimal designs, and modified by intermittent diffusion to avoid local solutions. Some simulations are given to support the theoretical results.

Suggested Citation

  • Yimin Huang & Xiangshun Kong & Mingyao Ai, 2020. "Optimal designs in sparse linear models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(2), pages 255-273, February.
    • Handle: RePEc:spr:metrik:v:83:y:2020:i:2:d:10.1007_s00184-019-00722-9
    DOI: 10.1007/s00184-019-00722-9
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    References listed on IDEAS

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    2. 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).
    3. Tingni Sun & Cun-Hui Zhang, 2012. "Scaled sparse linear regression," Biometrika, Biometrika Trust, vol. 99(4), pages 879-898.
    4. Cun-Hui Zhang & Stephanie S. Zhang, 2014. "Confidence intervals for low dimensional parameters in high dimensional linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 217-242, January.
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