Seyoung Park


Sep
10
2013

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  • Host Department: Statistics
  • Date: 09/10/2013
  • Time: 1:00PM

  • Location: 438 WH

  • Description:

    Much work has been done in the quantile regression analysis. The ordinary quantile regression
    estimation is asymptotically consistent when the number of predictors, p, is small, but
    it could be inconsistent if p grows with the sample size n. This motivates the use of penalization
    methods in model selection for quantile regression. Belloni and Chernozhukov
    (2011) consider the l1-penalized quantile regression in high dimensional sparse models and
    obtain some non-asymptotic results. Jiang (2012) introduces a new estimator that estimates
    several quantiles at the same time while penalizing inter-quantile differences as well as individual
    quantile coefficients, but provides no theoretical results for high dimensional predictors.
    In this work, we consider joint quantile regression in high-dimensional sparse
    models by allowing the number of quantiles, K, and the number of predictors, p, to grow
    with n. We provide asymptotic and non-asymptotic results on the penalized model selection
    and estimation procedures in the spirit of Jiang (2012), and study the oracle properties
    of adaptive penalization. We examine model selection consistency and stability across
    quantiles, and compare adaptive shrinkage with thresholding in the quantile regression
    framework.

  • Seyoung Park