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Statistical inference for high-dimensional models via recursive online-score estimation

Author

Listed:
  • Shi, Chengchun
  • Song, Rui
  • Lu, Wenbin
  • Li, Runzi

Abstract

In this article, we develop a new estimation and valid inference method for single or low-dimensional regression coefficients in high-dimensional generalized linear models. The number of the predictors is allowed to grow exponentially fast with respect to the sample size. The proposed estimator is computed by solving a score function. We recursively conduct model selection to reduce the dimensionality from high to a moderate scale and construct the score equation based on the selected variables. The proposed confidence interval (CI) achieves valid coverage without assuming consistency of the model selection procedure. When the selection consistency is achieved, we show the length of the proposed CI is asymptotically the same as the CI of the “oracle” method which works as well as if the support of the control variables were known. In addition, we prove the proposed CI is asymptotically narrower than the CIs constructed based on the desparsified Lasso estimator and the decorrelated score statistic. Simulation studies and real data applications are presented to back up our theoretical findings. Supplementary materials for this article are available online.

Suggested Citation

  • Shi, Chengchun & Song, Rui & Lu, Wenbin & Li, Runzi, 2020. "Statistical inference for high-dimensional models via recursive online-score estimation," LSE Research Online Documents on Economics 103043, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:103043
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    File URL: http://eprints.lse.ac.uk/103043/
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    References listed on IDEAS

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    1. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    2. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    3. Peter Bühlmann & Jacopo Mandozzi, 2014. "High-dimensional variable screening and bias in subsequent inference, with an empirical comparison," Computational Statistics, Springer, vol. 29(3), pages 407-430, June.
    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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    Cited by:

    1. Shi, Chengchun & Li, Lexin, 2022. "Testing mediation effects using logic of Boolean matrices," LSE Research Online Documents on Economics 108881, London School of Economics and Political Science, LSE Library.
    2. Alan Agresti & Sabrina Giordano & Anna Gottard, 2022. "A Review of Score-Test-Based Inference for Categorical Data," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 31-48, September.

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    More about this item

    Keywords

    confidence interval; Ultrahigh dimensions; Generalized linear models; online estimations; Online estimation; Confidence interval;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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