Abstract:

When estimating coefficients in a linear model, the (sparse) composite quantile regression proposed in Zou and Yuan (2008) serves as an efficient alternative to the (sparse) least squares to handle arbitrary errors. The highly nonsmooth nature of the composite loss in the sparse composite quantile regression makes its theoretical analysis as well as numerical computation much more challenging than the least squares method. The theory in Zou and Yuan (2008) was proven under fixed-dimension asymptotics and the estimator was computed via linear programming that does not scale well with high dimensions. We study the sparse composite quantile regression under ultrahigh dimensionality and make three contributions. First, we provide a non-asymptotic analysis of both the lasso and the folded concave penalized composite quantile regression, which reveals a practical way of achieving the oracle estimator. Second, we construct information criteria for selecting the regularization parameter in the folded concave penalized composite quantile regression and prove their selection consistency. Third, we exploit the structure of the composite loss and design a specialized optimization algorithm for computing the penalized composite quantile regression via the alternating direction method of multipliers. We conduct extensive simulations to illustrate the theoretical results.

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Topic: Colloquia: Department of Statistics and Actuarial Science, The University of Iowa

Time: May 6, 2021 03:15 PM Central Time (US and Canada)

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Meeting ID: 949 5289 2803