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Variable selection via composite quantile regression with dependent errors

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  • Yanlin Tang
  • Xinyuan Song
  • Zhongyi Zhu

Abstract

type="main" xml:id="stan12035-abs-0001"> We propose composite quantile regression for dependent data, in which the errors are from short-range dependent and strictly stationary linear processes. Under some regularity conditions, we show that composite quantile estimator enjoys root-n consistency and asymptotic normality. We investigate the asymptotic relative efficiency of composite quantile estimator to both single-level quantile regression and least-squares regression. When the errors have finite variance, the relative efficiency of composite quantile estimator with respect to the least-squares estimator has a universal lower bound. Under some regularity conditions, the adaptive least absolute shrinkage and selection operator penalty leads to consistent variable selection, and the asymptotic distribution of the non-zero coefficient is the same as that of the counterparts obtained when the true model is known. We conduct a simulation study and a real data analysis to evaluate the performance of the proposed approach.

Suggested Citation

  • Yanlin Tang & Xinyuan Song & Zhongyi Zhu, 2015. "Variable selection via composite quantile regression with dependent errors," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(1), pages 1-20, February.
    • Handle: RePEc:bla:stanee:v:69:y:2015:i:1:p:1-20
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    File URL: http://hdl.handle.net/10.1111/stan.12035
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    References listed on IDEAS

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    Cited by:

    1. Ping Yu & Ting Li & Zhongyi Zhu & Zhongzhan Zhang, 2019. "Composite quantile estimation in partial functional linear regression model with dependent errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(6), pages 633-656, August.
    2. Gabriela Ciuperca, 2018. "Test by adaptive LASSO quantile method for real-time detection of a change-point," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(6), pages 689-720, August.

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