Lack‐of‐fit tests for quantile regression models
将参数分位数回归模型的拟合不足检验转化为两个协变量条件分布是否相等的检验，并针对低维和高维数据分别构造了两种检验方法，后者在协变量数超过样本量时仍有效。
The paper novelly transforms lack‐of‐fit tests for parametric quantile regression models into checking the equality of two conditional distributions of covariates. Accordingly, by applying some successful two‐sample test statistics in the literature, two tests are constructed to check the lack of fit for low and high dimensional quantile regression models. The low dimensional test works well when the number of covariates is moderate, whereas the high dimensional test can maintain the power when the number of covariates exceeds the sample size. The null distribution of the high dimensional test has an explicit form, and the p‐values or critical values can then be calculated directly. The finite sample performance of the tests proposed is examined by simulation studies, and their usefulness is further illustrated by two real examples.