In this article, we revisit the problem of how to construct better nonparametric confidence intervals for the conditional quantile function from an optimization perspective. We apply the fully data‐driven bias correction procedure based on local polynomial smoothing to estimate the conditional quantile. To account for the effect of the estimated bias, we apply an asymptotic framework that the ratio of the bandwidth to the pilot bandwidth tends to some positive constant rather than zero as the sample size grows. We derive an alternative asymptotic normality of the proposed bias‐corrected quantile estimator as well as a new asymptotic variance formula. Based on theoretical results, two new pointwise confidence intervals are constructed through resampling strategies. Extensive simulation studies show that our proposed confidence intervals enjoy better performance than other competitors in terms of coverage probabilities and interval lengths and are not sensitive to the choice of bandwidth. Finally, our proposed procedure is further illustrated through United States' natality birth data in 2017.

中文翻译：

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通过稳健的偏差校正实现更好的非参数置信区间，以实现分位数回归

在本文中，我们从优化的角度重新审视了如何为条件分位数函数构造更好的非参数置信区间的问题。我们应用基于局部多项式平滑的完全数据驱动的偏差校正程序来估计条件分位数。为了考虑估计偏差的影响，我们采用渐近框架，即随着样本量的增加，带宽与导频带宽之比趋于某个正常数而不是零。我们导出了拟议的偏差校正分位数估计量的替代渐近正态性以及新的渐近方差公式。根据理论结果，通过重采样策略构造了两个新的逐点置信区间。大量的模拟研究表明，我们提出的置信区间在覆盖概率和区间长度方面比其他竞争者更好，并且对带宽的选择不敏感。最后，我们通过2017年美国的出生数据进一步说明了我们提出的程序。