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Local composite quantile regression smoothing: an efficient and safe alternative to local polynomial regression

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  • Bo Kai
  • Runze Li
  • Hui Zou

Abstract

Summary. Local polynomial regression is a useful non‐parametric regression tool to explore fine data structures and has been widely used in practice. We propose a new non‐parametric regression technique called local composite quantile regression smoothing to improve local polynomial regression further. Sampling properties of the estimation procedure proposed are studied. We derive the asymptotic bias, variance and normality of the estimate proposed. The asymptotic relative efficiency of the estimate with respect to local polynomial regression is investigated. It is shown that the estimate can be much more efficient than the local polynomial regression estimate for various non‐normal errors, while being almost as efficient as the local polynomial regression estimate for normal errors. Simulation is conducted to examine the performance of the estimates proposed. The simulation results are consistent with our theoretical findings. A real data example is used to illustrate the method proposed.

Suggested Citation

  • Bo Kai & Runze Li & Hui Zou, 2010. "Local composite quantile regression smoothing: an efficient and safe alternative to local polynomial regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 49-69, January.
    • Handle: RePEc:bla:jorssb:v:72:y:2010:i:1:p:49-69
    DOI: 10.1111/j.1467-9868.2009.00725.x
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    References listed on IDEAS

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    1. Koenker, Roger, 1984. "A note on L-estimates for linear models," Statistics & Probability Letters, Elsevier, vol. 2(6), pages 323-325, December.
    2. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
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