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A generalized Dantzig selector with shrinkage tuning

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  • Gareth M. James
  • Peter Radchenko

Abstract

The Dantzig selector performs variable selection and model fitting in linear regression. It uses an L 1 penalty to shrink the regression coefficients towards zero, in a similar fashion to the lasso. While both the lasso and Dantzig selector potentially do a good job of selecting the correct variables, they tend to overshrink the final coefficients. This results in an unfortunate trade-off. One can either select a high shrinkage tuning parameter that produces an accurate model but poor coefficient estimates or a low shrinkage parameter that produces more accurate coefficients but includes many irrelevant variables. We extend the Dantzig selector to fit generalized linear models while eliminating overshrinkage of the coefficient estimates, and develop a computationally efficient algorithm, similar in nature to least angle regression, to compute the entire path of coefficient estimates. A simulation study illustrates the advantages of our approach relative to others. We apply the methodology to two datasets. Copyright 2009, Oxford University Press.

Suggested Citation

  • Gareth M. James & Peter Radchenko, 2009. "A generalized Dantzig selector with shrinkage tuning," Biometrika, Biometrika Trust, vol. 96(2), pages 323-337.
  • Handle: RePEc:oup:biomet:v:96:y:2009:i:2:p:323-337
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    File URL: http://hdl.handle.net/10.1093/biomet/asp013
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    Cited by:

    1. Mkhadri, Abdallah & Ouhourane, Mohamed, 2013. "An extended variable inclusion and shrinkage algorithm for correlated variables," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 631-644.
    2. Laurin Charles & Boomsma Dorret & Lubke Gitta, 2016. "The use of vector bootstrapping to improve variable selection precision in Lasso models," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 15(4), pages 305-320, August.
    3. Bergersen Linn Cecilie & Glad Ingrid K. & Lyng Heidi, 2011. "Weighted Lasso with Data Integration," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-29, August.
    4. Brent A. Johnson & Qi Long & Matthias Chung, 2011. "On Path Restoration for Censored Outcomes," Biometrics, The International Biometric Society, vol. 67(4), pages 1379-1388, December.
    5. Faisal Maqbool Zahid & Gerhard Tutz, 2013. "Proportional Odds Models with High‐Dimensional Data Structure," International Statistical Review, International Statistical Institute, vol. 81(3), pages 388-406, December.
    6. Faisal Zahid & Gerhard Tutz, 2013. "Ridge estimation for multinomial logit models with symmetric side constraints," Computational Statistics, Springer, vol. 28(3), pages 1017-1034, June.
    7. Feng Li & Lu Lin & Yuxia Su, 2013. "Variable selection and parameter estimation for partially linear models via Dantzig selector," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(2), pages 225-238, February.
    8. Antoniadis, Anestis & Fryzlewicz, Piotr & Letué, Frédérique, 2010. "The Dantzig selector in Cox's proportional hazards model," LSE Research Online Documents on Economics 30992, London School of Economics and Political Science, LSE Library.
    9. Anestis Antoniadis & Piotr Fryzlewicz & Frédérique Letué, 2010. "The Dantzig Selector in Cox's Proportional Hazards Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 531-552, December.
    10. Luigi Augugliaro & Angelo M. Mineo & Ernst C. Wit, 2013. "Differential geometric least angle regression: a differential geometric approach to sparse generalized linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 471-498, June.

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