[PAST EVENT] Mathematics Colloquium and EXTREEMS-QED Lecture: Huixia (Judy) Wang (George Washington University)
Abstract: In this talk I will present a new marginal testing procedure to detect the presence of significant predictors associated with the quantiles of a scalar response. The idea is to fit the marginal quantile regression on each predictor separately, and then base the test on the t-statistic associated with the chosen most informative predictor at the quantile of interest. A resampling method is devised to calibrate this test statistic, which has non-regular limiting behavior due to the variable selection. 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 proposed test 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 using an application to an HIV drug resistance dataset.