Testing for Marginal Linear Effects in Quantile Regression
提出一种新的边际检验方法，通过逐个拟合分位数回归并基于最显著预测变量的t统计量来检测与响应变量条件分位数相关的预测变量，使用重抽样校准检验统计量，适用于高维数据且对异常值稳健。
Summary The paper develops a new marginal testing procedure to detect significant predictors that are associated with the conditional quantiles of a scalar response. The idea is to fit the marginal quantile regression on each predictor one at a time, and then to base the test on the t-statistics that are associated with the most predictive predictors. A resampling method is devised to calibrate this test statistic, which has non-regular limiting behaviour due to the selection of the most predictive variables. Asymptotic validity of the procedure is established in a general quantile regression setting in which the marginal quantile regression models can be misspecified. Even though a fixed dimension is assumed to derive the asymptotic results, the test proposed is applicable and computationally feasible for large dimensional predictors. The method is more flexible than existing marginal screening test methods based on mean regression and has the added advantage of being robust against outliers in the response. The approach is illustrated by using an application to a human immunodeficiency virus drug resistance data set.