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Controlling the false discoveries in LASSO

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  • Hanwen Huang

Abstract

The LASSO method estimates coefficients by minimizing the residual sum of squares plus a penalty term. The regularization parameter λ in LASSO controls the trade‐off between data fitting and sparsity. We derive relationship between λ and the false discovery proportion (FDP) of LASSO estimator and show how to select λ so as to achieve a desired FDP. Our estimation is based on the asymptotic distribution of LASSO estimator in the limit of both sample size and dimension going to infinity with fixed ratio. We use a factor analysis model to describe the dependence structure of the design matrix. An efficient majorization–minimization based algorithm is developed to estimate the FDP at fixed value of λ. The analytic results are compared with those of numerical simulations on finite‐size systems and are confirmed to be correct. An application to the high‐throughput genomic riboavin data set also demonstrates the usefulness of our method.

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  • Hanwen Huang, 2017. "Controlling the false discoveries in LASSO," Biometrics, The International Biometric Society, vol. 73(4), pages 1102-1110, December.
    • Handle: RePEc:bla:biomet:v:73:y:2017:i:4:p:1102-1110
    DOI: 10.1111/biom.12665
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    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. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    3. 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.
    4. 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.
    5. Liu, Yufeng & Hayes, David Neil & Nobel, Andrew & Marron, J. S, 2008. "Statistical Significance of Clustering for High-Dimension, Low–Sample Size Data," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1281-1293.
    6. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
    7. Efron, Bradley, 2007. "Correlation and Large-Scale Simultaneous Significance Testing," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 93-103, March.
    8. 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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    1. Masataka Taguri, 2022. "Discussion of “Akaike Memorial Lecture 2020: Some of the challenges of statistical applications”," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 643-647, August.

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