IDEAS home Printed from https://ideas.repec.org/a/taf/jnlasa/v110y2015i512p1422-1433.html
   My bibliography  Save this article

An Adaptive Resampling Test for Detecting the Presence of Significant Predictors

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01621459.2015.1095099
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/01621459.2015.1095099?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Meinshausen, Nicolai & Meier, Lukas & Bühlmann, Peter, 2009. "p-Values for High-Dimensional Regression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1671-1681.
    2. Tony Cai, T. & Jiang, Tiefeng, 2012. "Phase transition in limiting distributions of coherence of high-dimensional random matrices," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 24-39.
    3. Donald W. K. Andrews, 2000. "Inconsistency of the Bootstrap when a Parameter Is on the Boundary of the Parameter Space," Econometrica, Econometric Society, vol. 68(2), pages 399-406, March.
    4. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2011. "Inference on Treatment Effects After Selection Amongst High-Dimensional Controls," Papers 1201.0224, arXiv.org, revised May 2012.
    5. Laber, Eric B. & Murphy, Susan A., 2011. "Adaptive Confidence Intervals for the Test Error in Classification," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 904-913.
    6. 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.
    7. Yu I. Ingster & Alexandre B. Tsybakov & N. Verzelzn, 2010. "Detection Boundary in Sparse Regression," Working Papers 2010-28, Center for Research in Economics and Statistics.
    8. Richard Samworth, 2003. "A note on methods of restoring consistency to the bootstrap," Biometrika, Biometrika Trust, vol. 90(4), pages 985-990, December.
    9. Chatterjee, A. & Lahiri, S. N., 2011. "Bootstrapping Lasso Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 608-625.
    10. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
    11. Efron, Bradley, 2004. "Large-Scale Simultaneous Hypothesis Testing: The Choice of a Null Hypothesis," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 96-104, January.
    12. 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.
    13. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    14. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2013. "Supplementary Appendix for "Inference on Treatment Effects After Selection Amongst High-Dimensional Controls"," Papers 1305.6099, arXiv.org, revised Jun 2013.
    15. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Gonzalo, Jesús & Pitarakis, Jean-Yves, 2024. "Out-of-sample predictability in predictive regressions with many predictor candidates," International Journal of Forecasting, Elsevier, vol. 40(3), pages 1166-1178.
    4. Qing Zhou & Seunghyun Min, 2017. "Uncertainty quantification under group sparsity," Biometrika, Biometrika Trust, vol. 104(3), pages 613-632.
    5. Christis Katsouris, 2023. "High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods," Papers 2308.16192, arXiv.org.
    6. Giuseppe Cavaliere & Zeng-Hua Lu & Anders Rahbek & Yuhong Yang, 2021. "MinP Score Tests with an Inequality Constrained Parameter Space," Papers 2107.06089, arXiv.org.
    7. 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.
    8. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Ruggieri, Eric & Lawrence, Charles E., 2012. "On efficient calculations for Bayesian variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1319-1332.
    3. Joseph Antonelli & Matthew Cefalu & Nathan Palmer & Denis Agniel, 2018. "Doubly robust matching estimators for high dimensional confounding adjustment," Biometrics, The International Biometric Society, vol. 74(4), pages 1171-1179, December.
    4. Shuichi Kawano, 2014. "Selection of tuning parameters in bridge regression models via Bayesian information criterion," Statistical Papers, Springer, vol. 55(4), pages 1207-1223, November.
    5. Wang, Christina Dan & Chen, Zhao & Lian, Yimin & Chen, Min, 2022. "Asset selection based on high frequency Sharpe ratio," Journal of Econometrics, Elsevier, vol. 227(1), pages 168-188.
    6. Loann David Denis Desboulets, 2018. "A Review on Variable Selection in Regression Analysis," Econometrics, MDPI, vol. 6(4), pages 1-27, November.
    7. Lee, Ji Hyung & Shi, Zhentao & Gao, Zhan, 2022. "On LASSO for predictive regression," Journal of Econometrics, Elsevier, vol. 229(2), pages 322-349.
    8. Victor Chernozhukov & Christian Hansen & Yuan Liao, 2015. "A lava attack on the recovery of sums of dense and sparse signals," CeMMAP working papers CWP56/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. Jingxuan Luo & Lili Yue & Gaorong Li, 2023. "Overview of High-Dimensional Measurement Error Regression Models," Mathematics, MDPI, vol. 11(14), pages 1-22, July.
    10. Tan, Xin Lu, 2019. "Optimal estimation of slope vector in high-dimensional linear transformation models," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 179-204.
    11. Ricardo P. Masini & Marcelo C. Medeiros & Eduardo F. Mendes, 2023. "Machine learning advances for time series forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 76-111, February.
    12. Chen, Shi & Härdle, Wolfgang Karl & López Cabrera, Brenda, 2018. "Regularization Approach for Network Modeling of German Energy Market," IRTG 1792 Discussion Papers 2018-017, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    13. Zakariya Yahya Algamal & Muhammad Hisyam Lee, 2019. "A two-stage sparse logistic regression for optimal gene selection in high-dimensional microarray data classification," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(3), pages 753-771, September.
    14. Fan, Jianqing & Liao, Yuan, 2012. "Endogeneity in ultrahigh dimension," MPRA Paper 38698, University Library of Munich, Germany.
    15. Min Chen & Yimin Lian & Zhao Chen & Zhengjun Zhang, 2017. "Sure explained variability and independence screening," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 849-883, October.
    16. Minerva Mukhopadhyay & David B. Dunson, 2020. "Targeted Random Projection for Prediction From High-Dimensional Features," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 1998-2010, December.
    17. Ertefaie Ashkan & Asgharian Masoud & Stephens David A., 2018. "Variable Selection in Causal Inference using a Simultaneous Penalization Method," Journal of Causal Inference, De Gruyter, vol. 6(1), pages 1-16, March.
    18. Dai, Linlin & Chen, Kani & Sun, Zhihua & Liu, Zhenqiu & Li, Gang, 2018. "Broken adaptive ridge regression and its asymptotic properties," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 334-351.
    19. Zhao, Shaofei & Fu, Guifang, 2022. "Distribution-free and model-free multivariate feature screening via multivariate rank distance correlation," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    20. Aneiros, Germán & Novo, Silvia & Vieu, Philippe, 2022. "Variable selection in functional regression models: A review," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:jnlasa:v:110:y:2015:i:512:p:1422-1433. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UASA20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.