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Preprint No.SS-2025-0220
Manuscript IDSS-2025-0220
Complete AuthorsYang Li, Zemin Zheng, Jia Zhou, Ziwei Zhu
Corresponding AuthorsJia Zhou
Emailstszhjia@mail.ustc.edu.cn

References

  1. Bellec, P. C. and Zhang, C.-H. (2022). De-biasing the lasso with degrees-of-freedom adjustment. Bernoulli 28(2), 713–743.
  2. Bickel, P. J., Ritov, Y. and Tsybakov, A. B. (2009). Simultaneous analysis of Lasso and Dantzig selector. Ann. Statist. 37(4), 1705–1732.
  3. Cai, T. T. and Guo, Z. (2017). Confidence intervals for high-dimensional linear regression: Minimax rates and adaptivity. Ann. Statist. 45(2), 615–646.
  4. Chen, K. and Zhang, Y. (2025). Semi-supervised linear regression: enhancing efficiency and robustness in high dimensions. Biometrics 81(3), ujaf113.
  5. Fan, J. and Lv, J. (2008). Sure independence screening for ultrahigh dimensional feature space. J. R. Stat. Soc. Ser. B. Stat. Methodol. 70(5), 849–911.
  6. Fan, Y., Demirkaya, E. and Lv, J. (2019). Nonuniformity of p-values can occur early in diverging dimensions. J. Mach. Learn. Res. 20(77), 1–33.
  7. Fan, Y., Jin, J. and Yao, Z. (2013). Optimal classification in sparse Gaussian graphic model. Ann. Statist. 41(5), 2537–2571.
  8. Fan, Y., Kong, Y., Li, D. and Zheng, Z. (2015). Innovated interaction screening for high-dimensional nonlinear classification. Ann. Statist. 43(3), 1243–1272.
  9. Fan, Y. and Lv, J. (2014). Asymptotic properties for combined L1 and concave regularization. Biometrika 101(1), 57–70.
  10. Fan, Y. and Tang, C. (2013). Tuning parameter selection in high dimensional penalized likelihood. J. R. Stat. Soc. Ser. B. Stat. Methodol. 75(3), 531–552.
  11. Jankov´a, J., Shah, R. D., B¨uhlmann, P. and Samworth, R. J. (2020). Goodness-of-fit testing in high dimensional generalized linear models. J. R. Stat. Soc. Ser. B. Stat. Methodol. 82(3), 773–795.
  12. Javanmard, A. and Montanari, A. (2014). Confidence intervals and hypothesis testing for high-dimensional regression. J. Mach. Learn. Res. 15(82), 2869–2909.
  13. Javanmard, A. and Montanari, A. (2018). Debiasing the Lasso: Optimal sample size for Gaussian designs. Ann. Statist. 46(6A), 2593–2622.
  14. Kong, Y., Zheng, Z. and Lv, J. (2016). The constrained Dantzig selector with enhanced consistency. J. Mach. Learn. Res. 17(123), 1–22.
  15. Li, R., Zhong, W. and Zhu, L. (2012). Feature screening via distance correlation learning. J. Amer. Statist. Assoc. 107(499), 1129–1139.
  16. Rapach, D. E., Ringgenberg, M. C. and Zhou, G. (2016). Short interest and aggregate stock returns. J. Financ. Econ. 121(1), 46–65.
  17. Shinkyu, A. and Sueishi, N. (2025). Small tuning parameter selection for the debiased lasso. J. Bus. Econom. Statist. 43(4), 872–883.
  18. Sun, T. and Zhang, C.-H. (2012). Scaled sparse linear regression. Biometrika 99(4), 879–898.
  19. Sur, P., Chen, Y. and Cand`es, E. (2020). The likelihood ratio test in high-dimensional logistic regression is asymptotically a rescaled chi-square. Probability Theory and Related Fields, 175(1–2), 487–558.
  20. Tian, X. and Taylor, J. (2018). Selective inference with a randomized response. Ann. Statist. 46(2), 679–710.
  21. Tibshirani, R. (1996). Regression shrinkage and selection via the Lasso. J. R. Stat. Soc. Ser. B. Stat. Methodol. 58(1), 267–288.
  22. Tibshirani, R. J., Taylor, J., Lockhart, R. and Tibshirani, R. (2016). Exact post-selection inference for sequential regression procedures. J. Amer. Statist. Assoc. 111(514), 600–620.
  23. van de Geer, S., B¨uhlmann, P., Ritov, Y. and Dezeure, R. (2014). On asymptotically optimal confidence regions and tests for high-dimensional models. Ann. Statist. 42(3), 1166–1202.
  24. Vazquez, O. and Nan, B. (2025). Debiased lasso after sample splitting for estimation and inference in highdimensional generalized linear models. Can J Stat. 53(1), e11827.
  25. Wainwright, M. J. (2009). Information-theoretic limits on sparsity recovery in the high-dimensional and noisy setting. IEEE Trans. Inform. Theory 55(12), 5728–5741.
  26. Wang, X. and Leng, C. (2016). High dimensional ordinary least squares projection for screening variables. J. R. Stat. Soc. Ser. B. Stat. Methodol. 78(3), 589–611.
  27. Ye, F. and Zhang, C.-H. (2010). Rate minimaxity of the Lasso and Dantzig selector for the ℓq loss in ℓr balls. J. Mach. Learn. Res. 11(114), 3519–3540.
  28. Zhang, C.-H. (2010). Nearly unbiased variable selection under minimax concave penalty. Ann. Statist. 38(2), 894–942.
  29. Zhang, C.-H. and Zhang, S. S. (2014). Confidence intervals for low dimensional parameters in high dimensional linear models. J. R. Stat. Soc. Ser. B. Stat. Methodol. 76(1), 217–242.
  30. Zhou, K., Li, K.-C. and Zhou, Q. (2023). Honest confidence sets for high-dimensional regression by projection and shrinkage. J. Amer. Statist. Assoc. 118(541), 469–488.

Acknowledgments

This research has been supported by the National Key Research and Development Program of China (2022YFA1008000), the Natural Science Foundation of China (72571258;

12526560), the Anhui Provincial Natural Science Foundation (JZ2025AKZR0533), the

Natural Science Foundation of Hefei University of Technology (JZ2025HGTA0143), and

the Fundamental Research Funds for the Central Universities (WK2040000114).

Supplementary Materials

The extension of HOT to sub-Gaussian designs and all technical details are relegated to

the Supplementary Material for this paper.

Supplementary materials are available for download.