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An Adaptive Resampling Test for Detecting the Presence of Significant Predictors

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  • Ian W. McKeague
  • Min Qian

Abstract

This article investigates marginal screening for detecting the presence of significant predictors in high-dimensional regression. Screening large numbers of predictors is a challenging problem due to the nonstandard limiting behavior of post-model-selected estimators. There is a common misconception that the oracle property for such estimators is a panacea, but the oracle property only holds away from the null hypothesis of interest in marginal screening. To address this difficulty, we propose an adaptive resampling test (ART). Our approach provides an alternative to the popular (yet conservative) Bonferroni method of controlling family-wise error rates. ART is adaptive in the sense that thresholding is used to decide whether the centered percentile bootstrap applies, and otherwise adapts to the nonstandard asymptotics in the tightest way possible. The performance of the approach is evaluated using a simulation study and applied to gene expression data and HIV drug resistance data.

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  • Ian W. McKeague & Min Qian, 2015. "An Adaptive Resampling Test for Detecting the Presence of Significant Predictors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1422-1433, December.
    • Handle: RePEc:taf:jnlasa:v:110:y:2015:i:512:p:1422-1433
    DOI: 10.1080/01621459.2015.1095099
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    References listed on IDEAS

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    Cited by:

    1. Christis Katsouris, 2023. "High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods," Papers 2308.16192, arXiv.org.
    2. Ying Huang & Juhee Cho & Youyi Fong, 2021. "Threshold‐based subgroup testing in logistic regression models in two‐phase sampling designs," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(2), pages 291-311, March.
    3. Gonzalo, Jesús & Pitarakis, Jean-Yves, 2020. "Out of sample predictability in predictive regressions with many predictor candidates," UC3M Working papers. Economics 31554, Universidad Carlos III de Madrid. Departamento de Economía.
    4. Youyi Fong & Chongzhi Di & Ying Huang & Peter B. Gilbert, 2017. "Model-robust inference for continuous threshold regression models," Biometrics, The International Biometric Society, vol. 73(2), pages 452-462, June.
    5. Ruben Dezeure & Peter Bühlmann & Cun-Hui Zhang, 2017. "High-dimensional simultaneous inference with the bootstrap," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(4), pages 685-719, December.
    6. Songqiao Tang & Huiyu Wang & Guanao Yan & Lixin Zhang, 2023. "Empirical likelihood based tests for detecting the presence of significant predictors in marginal quantile regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(2), pages 149-179, February.
    7. Qing Zhou & Seunghyun Min, 2017. "Uncertainty quantification under group sparsity," Biometrika, Biometrika Trust, vol. 104(3), pages 613-632.
    8. Giuseppe Cavaliere & Zeng-Hua Lu & Anders Rahbek & Yuhong Yang, 2021. "MinP Score Tests with an Inequality Constrained Parameter Space," Papers 2107.06089, arXiv.org.

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