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Robust sure independence screening for nonpolynomial dimensional generalized linear models

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  • Abhik Ghosh
  • Erica Ponzi
  • Torkjel Sandanger
  • Magne Thoresen

Abstract

We consider the problem of variable screening in ultra‐high‐dimensional generalized linear models (GLMs) of nonpolynomial orders. Since the popular SIS approach is extremely unstable in the presence of contamination and noise, we discuss a new robust screening procedure based on the minimum density power divergence estimator (MDPDE) of the marginal regression coefficients. Our proposed screening procedure performs well under pure and contaminated data scenarios. We provide a theoretical motivation for the use of marginal MDPDEs for variable screening from both population as well as sample aspects; in particular, we prove that the marginal MDPDEs are uniformly consistent leading to the sure screening property of our proposed algorithm. Finally, we propose an appropriate MDPDE‐based extension for robust conditional screening in GLMs along with the derivation of its sure screening property. Our proposed methods are illustrated through extensive numerical studies along with an interesting real data application.

Suggested Citation

  • Abhik Ghosh & Erica Ponzi & Torkjel Sandanger & Magne Thoresen, 2023. "Robust sure independence screening for nonpolynomial dimensional generalized linear models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(3), pages 1232-1262, September.
    • Handle: RePEc:bla:scjsta:v:50:y:2023:i:3:p:1232-1262
    DOI: 10.1111/sjos.12628
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    References listed on IDEAS

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    1. Emre Barut & Jianqing Fan & Anneleen Verhasselt, 2016. "Conditional Sure Independence Screening," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1266-1277, July.
    2. Ayanendranath Basu & Abhik Ghosh & Abhijit Mandal & Nirian Martin & Leandro Pardo, 2021. "Robust Wald-type tests in GLM with random design based on minimum density power divergence estimators," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 973-1005, September.
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    5. Weiyan Mu & Shifeng Xiong, 2014. "Some notes on robust sure independence screening," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(10), pages 2092-2102, October.
    6. Zhao, Sihai Dave & Li, Yi, 2012. "Principled sure independence screening for Cox models with ultra-high-dimensional covariates," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 397-411.
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