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Activity Number: 124
Type: Contributed
Date/Time: Monday, August 1, 2016 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract #321372
Title: Bernstein-Von Mises Theorem for Individual Entries in Sparse High-Dimensional Linear Regression
Author(s): Dana Yang*
Companies: Yale University
Keywords: Bernstein-von Mises ; sparse linear regression ; Bayesian statistics

We consider the sparse high dimensional linear regression model Y=Xb+Z where b is a sparse vector. For this problem, Bayesian posterior contraction results have been shown, according to which if the prior is suitably chosen, the posterior distribution of b puts most of its mass in a small neighborhood near the truth. However there have been few results about the shape of that posterior distribution. We were able to give a prior distribution for b such that under the truth, the posterior marginal distribution of a single entry b_i is asymptotically normal with its mean equal to an efficient estimator and its variance close to the Fisher information at the truth. Based on this Bernstein-von Mises phenomenon, one could deduce that Bayesian credible interval matches with the frequentist confidence interval constructed from an efficient estimator for b_i.

Authors who are presenting talks have a * after their name.

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