Posterior asymptotic normality for an individual coordinate in high-dimensional linear regression

Abstract

It is well known that high-dimensional procedures like the LASSO provide biased estimators of parameters in a linear model. In a 2014 paper Zhang and Zhang showed how to remove this bias by means of a two-step procedure. We show that de-biasing can also be achieved by a one-step estimator, the form of which inspires the development of a Bayesian analogue of the frequentists’ de-biasing techniques.