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The growth rate of significant regressors for high dimensional data

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  • Zheng, Qi
  • Gallagher, Colin
  • Kulasekera, K.B.

Abstract

We give a new consistency proof for high-dimensional quantile regression estimators. A consequence of this proof is that the number of significant regressors can grow at a rate slog2(s)=o(n). To our best knowledge, this is the fastest rate achieved for high-dimensional quantile regression.

Suggested Citation

  • Zheng, Qi & Gallagher, Colin & Kulasekera, K.B., 2013. "The growth rate of significant regressors for high dimensional data," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 1969-1972.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:9:p:1969-1972
    DOI: 10.1016/j.spl.2013.04.029
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    References listed on IDEAS

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    1. 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.
    2. He, Xuming & Shao, Qi-Man, 2000. "On Parameters of Increasing Dimensions," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 120-135, April.
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