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Title: A conditional marginal test in high-dimensional quantile regression Authors:  Yanlin Tang - TONGJI University (China) [presenting]
Yinfeng Wang - Shanghai Dianji University (China)
Huixia Wang - The George Washington University (United States)
Qing Pan - George Washington University (United States)
Abstract: A conditional marginal score-type test in high-dimensional quantile regression is proposed in order to test the presence of significant covariates given a conditioning set. The test is based on the maximal score-type test statistics, and under mild regularity conditions, the proposed test statistic converges to a type I extreme value distribution, after some standardization. Besides the asymptotic distribution, we also propose a multiplier bootstrap method for critical value construction. We also illustrate how the proposed test can be used as a stopping rule in forward regression. We show, through simulation, that the proposed method provides adequate control of the family-wise error rate with competitive power. We illustrate the application of our method by analyzing a GFR data.