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Lasso, knockoff and Gaussian covariates: a comparison

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  • Davies, Laurie

Abstract

Given data y and k covariates xj one problem in linear regression is to decide which if any of the covariates to include when regressing the dependent variable y on the covariates xj . In this paper three such methods, lasso, knockoff and Gaussian covariates are compared using simulations and real data. The Gaussian covariate method is based on exact probabilities which are valid for all y and xj making it model free. Moreover the probabilities agree with those based on the F-distribution for the standard linear model with i.i.d. Gaussian errors. It is conceptually, mathematically and algorithmically very simple, it is very fast and makes no use of simulations. It outperforms lasso and knockoff in all respects by a considerable margin.

Suggested Citation

  • Davies, Laurie, 2018. "Lasso, knockoff and Gaussian covariates: a comparison," IRTG 1792 Discussion Papers 2018-019, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    • Handle: RePEc:zbw:irtgdp:2018019
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    Cited by:

    1. Qingliang Fan & Wei Zhong, 2018. "Nonparametric Additive Instrumental Variable Estimator: A Group Shrinkage Estimation Perspective," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(3), pages 388-399, July.
    2. Victor Chernozhukov & Wolfgang K. Hardle & Chen Huang & Weining Wang, 2018. "LASSO-Driven Inference in Time and Space," Papers 1806.05081, arXiv.org, revised May 2020.
    3. Zhong, Wei & Liu, Xi & Ma, Shuangge, 2018. "Variable selection and direction estimation for single-index models via DC-TGDR method," IRTG 1792 Discussion Papers 2018-050, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    4. Guo, Li & Tao, Yubo & Härdle, Wolfgang Karl, 2018. "Understanding Latent Group Structure of Cryptocurrencies Market: A Dynamic Network Perspective," IRTG 1792 Discussion Papers 2018-032, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    5. Packham, Natalie & Woebbeking, Fabian, 2018. "A factor-model approach for correlation scenarios and correlation stress-testing," IRTG 1792 Discussion Papers 2018-034, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    6. Xiaojia Bao & Qingliang Fan, 2020. "The impact of temperature on gaming productivity: evidence from online games," Empirical Economics, Springer, vol. 58(2), pages 835-867, February.
    7. Packham, Natalie & Kalkbrener, Michael & Overbeck, Ludger, 2018. "Default probabilities and default correlations under stress," IRTG 1792 Discussion Papers 2018-037, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    8. Kuczmaszewska, Anna & Yan, Ji Gao, 2018. "On complete convergence in Marcinkiewicz-Zygmund type SLLN for random variables," IRTG 1792 Discussion Papers 2018-041, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    9. Chen, Haiqiang & Li, Yingxing & Lin, Ming & Zhu, Yanli, 2018. "A Regime Shift Model with Nonparametric Switching Mechanism," IRTG 1792 Discussion Papers 2018-048, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    10. Yatracos, Yannis G., 2018. "Residual'S Influence Index (Rinfin), Bad Leverage And Unmasking In High Dimensional L2-Regression," IRTG 1792 Discussion Papers 2018-060, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    11. Zbonakova, Lenka & Li, Xinjue & Härdle, Wolfgang Karl, 2018. "Penalized Adaptive Forecasting with Large Information Sets and Structural Changes," IRTG 1792 Discussion Papers 2018-039, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    12. Packham, Natalie, 2018. "Optimal contracts under competition when uncertainty from adverse selection and moral hazard are present," IRTG 1792 Discussion Papers 2018-033, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    13. Cai, Zongwu & Fang, Ying & Lin, Ming & Su, Jia, 2018. "Inferences for a Partially Varying Coefficient Model With Endogenous Regressors," IRTG 1792 Discussion Papers 2018-047, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    14. Wang, Honglin & Yu, Fan & Zhou, Yinggang, 2018. "Property Investment and Rental Rate under Housing Price Uncertainty: A Real Options Approach," IRTG 1792 Discussion Papers 2018-051, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    15. Yan, Ji Gao, 2018. "Complete Convergence and Complete Moment Convergence for Maximal Weighted Sums of Extended Negatively Dependent Random Variables," IRTG 1792 Discussion Papers 2018-040, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    16. Kalkbrener, Michael & Packham, Natalie, 2018. "Correlation Under Stress In Normal Variance Mixture Models," IRTG 1792 Discussion Papers 2018-035, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    17. Chiu, Hsin-Yu & Chiang, Mi-Hsiu & Kuo, Wei-Yu, 2018. "Predicative Ability of Similarity-based Futures Trading Strategies," IRTG 1792 Discussion Papers 2018-045, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    18. Guo, Shaojun & Li, Dong & Li, Muyi, 2018. "Strict Stationarity Testing and GLAD Estimation of Double Autoregressive Models," IRTG 1792 Discussion Papers 2018-049, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    19. Koziuk, Andzhey & Spokoiny, Vladimir, 2018. "Toolbox: Gaussian comparison on Eucledian balls," IRTG 1792 Discussion Papers 2018-028, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".

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    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General

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