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Variable selection and parameter estimation for partially linear models via Dantzig selector

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  • Feng Li
  • Lu Lin
  • Yuxia Su

Abstract

Variable selection plays an important role in the high dimensionality data analysis, the Dantzig selector performs variable selection and model fitting for linear and generalized linear models. In this paper we focus on variable selection and parametric estimation for partially linear models via the Dantzig selector. Large sample asymptotic properties of the Dantzig selector estimator are studied when sample size n tends to infinity while p is fixed. We see that the Dantzig selector might not be consistent. To remedy this drawback, we take the adaptive Dantzig selector motivated by Dicker and Lin (submitted). Moreover, we obtain that the adaptive Dantzig selector estimator for the parametric component of partially linear models has the oracle properties under some appropriate conditions. As generalizations of the Dantzig selector, both the adaptive Dantzig selector and the Dantzig selector optimization can be implemented by the efficient algorithm DASSO proposed by James et al. (J R Stat Soc Ser B 71:127–142, 2009 ). Choices of tuning parameter and bandwidth are also discussed. Copyright Springer-Verlag 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:76:y:2013:i:2:p:225-238
    DOI: 10.1007/s00184-012-0384-x
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    References listed on IDEAS

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    1. Gareth M. James & Peter Radchenko & Jinchi Lv, 2009. "DASSO: connections between the Dantzig selector and lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 127-142, January.
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