Composite quantile regression for single-index models with asymmetric errors

Jing Sun ()
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Jing Sun: Ludong University

Computational Statistics, 2016, vol. 31, issue 1, No 15, 329-351

Abstract: Abstract For the single-index model, a composite quantile regression technique is proposed in this paper to construct robust and efficient estimation. Theoretical analysis reveals that the proposed estimate of the single-index vector is highly efficient relative to its corresponding least squares estimate. For the single-index vector, the proposed method is always valid across a wide spectrum of error distributions; even in the worst case scenario, the asymptotic relative efficiency has a lower bound 86.4 %. Meanwhile, we employ weighted local composite quantile regression to obtain a consistent and robust estimate for the nonparametric component in the single-index model, which is adapted to both symmetric and asymmetric distributions. Numerical study and a real data analysis can further illustrate our theoretical findings.

Keywords: Composite quantile regression; Single-index model; Asymptotic relative efficiency; Symmetric and asymmetric distributions; Optimal weight vector (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s00180-016-0645-7

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