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Composite quantile regression for single-index models with asymmetric errors

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  • Jing Sun

    (Ludong University)

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.

Suggested Citation

  • Jing Sun, 2016. "Composite quantile regression for single-index models with asymmetric errors," Computational Statistics, Springer, vol. 31(1), pages 329-351, March.
    • Handle: RePEc:spr:compst:v:31:y:2016:i:1:d:10.1007_s00180-016-0645-7
    DOI: 10.1007/s00180-016-0645-7
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