论文标题
基于分位数模态回归的引导性推断
Bootstrap inference for quantile-based modal regression
论文作者
论文摘要
在本文中，我们基于分位数回归开发了条件模式的统一推理方法。具体而言，我们建议通过将线性分位数回归估计器平滑定义的估计条件分位数函数的导数降至最低，并开发两种bootstrap方法，即我们的条件模式估算器，从而定义了估计的条件分位数函数，并开发了两种bootstrap方法，一种新型的枢轴引导程序和非参数bootstrap。在高维高斯近似技术的基础上，我们确定了条件模式的两种bootstrap方法构建的同时置信矩形的有效性。我们还将前面的分析扩展到协变量矢量的维度随样本量增加的情况。最后，我们使用美国工资数据进行了模拟实验和实际数据分析，以证明我们的推理方法的有限样本性能。
In this paper, we develop uniform inference methods for the conditional mode based on quantile regression. Specifically, we propose to estimate the conditional mode by minimizing the derivative of the estimated conditional quantile function defined by smoothing the linear quantile regression estimator, and develop two bootstrap methods, a novel pivotal bootstrap and the nonparametric bootstrap, for our conditional mode estimator. Building on high-dimensional Gaussian approximation techniques, we establish the validity of simultaneous confidence rectangles constructed from the two bootstrap methods for the conditional mode. We also extend the preceding analysis to the case where the dimension of the covariate vector is increasing with the sample size. Finally, we conduct simulation experiments and a real data analysis using U.S. wage data to demonstrate the finite sample performance of our inference method.
