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Title: Inference for high-dimensional models Authors:  Yi Li - University of Michigan (United States) [presenting]
Abstract: Inference for high-dimensional models is challenging as penalization and selection are often involved. A novel way of simultaneous estimation and inference for high-dimensional linear models is proposed. By smoothing over partial regression estimates based on some variable selection scheme, we reduce the problem to a low-dimensional case such as fitting least squares. The procedure, termed as Selection-assisted Partial Regression and Smoothing (SPARES), utilizes data-splitting with bootstrap, variable selection, and partial regression. We show that the SPARES estimator is asymptotically unbiased and normal, and derive its variance via a non-parametric delta method. The utility of the procedure is evaluated under various simulation scenarios and via comparisons with some competing methods, the de-biased LASSO estimators. We apply the method to analyze two genomic datasets.