Biometrics

Drawing inferences for high‐dimensional linear models: A selection‐assisted partial regression and smoothing approach

Early View

Abstract Drawing inferences for high‐dimensional models is challenging as regular asymptotic theories are not applicable. This article proposes a new framework of simultaneous estimation and inferences for high‐dimensional linear models. By smoothing over partial regression estimates based on a given variable selection scheme, we reduce the problem to low‐dimensional least squares estimations. 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 two genomic datasets and obtain biologically meaningful results.

Related Topics

Related Publications

Related Content

Site Footer

Address:

This website is provided by John Wiley & Sons Limited, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ (Company No: 00641132, VAT No: 376766987)

Published features on StatisticsViews.com are checked for statistical accuracy by a panel from the European Network for Business and Industrial Statistics (ENBIS)   to whom Wiley and StatisticsViews.com express their gratitude. This panel are: Ron Kenett, David Steinberg, Shirley Coleman, Irena Ograjenšek, Fabrizio Ruggeri, Rainer Göb, Philippe Castagliola, Xavier Tort-Martorell, Bart De Ketelaere, Antonio Pievatolo, Martina Vandebroek, Lance Mitchell, Gilbert Saporta, Helmut Waldl and Stelios Psarakis.