Empirical likelihood based tests for detecting the presence of significant predictors in marginal quantile regression

This article investigates detecting the presence of significant predictors in marginal quantile regression. The main idea comes from the connection between the quantile correlation and the slope parameter of the marginal quantile regression, which is quite different from other methods. By introducing the local linear model and the plug-in empirical likelihood method, consistent asymptotic distribution and its adjusted version are obtained. We not only circumvent the non-regularity encountered by post-model-selected estimators but also make the results more concise. Two adaptive resampling test procedures are proposed in practice by comparing the t-statistics with a threshold to decide whether to use the traditional centered percentile bootstrap or otherwise adapt to the asymptotic distribution under the local model. Simulation studies compare these two resampling tests with other competing methods in several cases. Results show that the approaches proposed are more robust for each quantile level and can control type I error well. Two real datasets from Forbes magazine and the HIV drug resistance database are also applied to illustrate the new methods.