Title: Global Inference for High-Dimensional Quantile Regression with Heterogeneity
Seminar Speaker: Tate Jacobson, Assistant Professor, Department of Statistics, Oregon State University.
In recent decades high-dimensional data have become commonplace in domains from economics to genomics. Among methods extended and adapted for the high-dimensional setting, quantile regression has received significant attention due to its well-known robustness to outliers and ability to accommodate heteroscedastic errors. Despite this considerable interest, the inferential tools that have been developed for high-dimensional quantile regression have significant limitations—being limited to testing simple hypotheses, only making inferences for a single quantile at a time, or assuming a homoscedastic error model. To broaden the scope of statistical questions that can be answered in high-dimensional quantile regression, we introduce partial penalized tests for the quantile regression process which can be used to test any linear hypothesis, provide inferences over a set of quantiles, and allow for heteroscedastic errors. We propose a novel globally adaptive local linear approximation (LLA) algorithm to compute the partial penalized estimators used in our tests and prove that the LLA solutions possess the strong oracle property with respect to “testing oracles”. Using this strong oracle result, we establish asymptotic guarantees for the partial penalized tests evaluated at the LLA solutions.