Uniform Asymptotics for Nonparametric Quantile Regression with an Application to Testing Monotonicity
Uniform Asymptotics for Nonparametric Quantile Regression with an Application to Testing Monotonicity
复制标题
非参数分位数回归的一致渐近及其在测试单调性中的应用
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Yoon
中科院分区：
文献类型：
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作者：
S. Lee;Kyungchul Song;Yoon
本文建立了分位数回归函数的局部多项式估计量的一致误差率。错误率在分位数范围内、回归量的评估点范围内以及观察到的随机变量的广泛概率类别内是均匀的。现有的关于局部多项式分位数回归估计的Bahadur表示的结果大多适用于固定数据生成过程。在检验单调性的背景下，零假设是一个复杂的复合假设，建立在一大类数据生成过程中保持一致的Bahadur展开是特别相关的。此外，我们建立了相同错误率的自举局部多项式估计，这可以用于各种自举推理。为了说明这一点，我们应用于测试分位数回归的单调性，并在此基础上给出了蒙特卡罗实验。
In this paper, we establish a uniform error rate of a Bahadur representation for local polynomial estimators of quantile regression functions. The error rate is uniform over a range of quantiles, a range of evaluation points in the regressors, and over a wide class of probabilities for observed random variables. Most of the existing results on Bahadur representations for local polynomial quantile regression estimators apply to the fixed data generating process. In the context of testing monotonicity where the null hypothesis is of a complex composite hypothesis, it is particularly relevant to establish Bahadur expansions that hold uniformly over a large class of data generating processes. In addition, we establish the same error rate for bootstrap local polynomial estimators which can be useful for various bootstrap inference. As an illustration, we apply to testing monotonicity of quantile regression and present Monte Carlo experiments based on this example.