Adaptive posterior concentration rates for sparse high-dimensional linear regression with random design and unknown error variance
Year: 2024
Type: preprint
Abstract: This paper investigates sparse high-dimensional linear regression, particularly examining the properties of the posterior under conditions of random design and unknown error variance. We provide consistency results for the posterior and analyze its concentration rates, demonstrating adaptiveness to the unknown sparsity level of the regression coefficient vector. Furthermore, we extend our investigation to establish concentration outcomes for parameter estimation using specific distance measures. These findings are in line with recent discoveries in frequentist studies. Additionally, by employing techniques to address model misspecification through a fractional posterior, we broaden our analysis through oracle inequalities to encompass the critical aspect of model misspecification for the regular posterior. Our novel findings are demonstrated using two different types of sparsity priors: a shrinkage prior and a spike-and-slab prior.
Source: arXiv (Cornell University)
Author: Mai, The Tien
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Norges Forskningsråd
Award: G7275849276
OpenAlex ID: W4399198428