Title: Drawing inferences for high-dimensional linear models: A selection-assisted partial regression and smoothing approach
Authors: Yi Li - University of Michigan (United States) [presenting]
Abstract: Drawing inferences for high-dimensional models is challenging as regular asymptotic theories are not applicable. A new framework of simultaneous estimation and inferences for high-dimensional linear models is proposed. By smoothing over partial regression estimates based on a given variable selection scheme, we reduce the problem to a low-dimensional least squares estimation. The procedure, termed as Selection-assisted Partial Regression and Smoothing (SPARES), utilizes data splitting along with variable selection and partial regression. We show that the SPARES estimator is asymptotically unbiased and normal, and derive its variance via a nonparametric delta method. The utility of the procedure is evaluated under various simulation scenarios and via comparisons with the de-biased LASSO estimators, a major competitor. We apply the method to analyze a genomic dataset and obtain biologically meaningful results.