Date of this Version
The Annals of Statistics
This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix estimation and noisy matrix completion. We propose computationally feasible convex programs for statistical inference including estimation, confidence intervals and hypothesis testing. A theoretical framework is developed to characterize the local estimation rate of convergence and to provide statistical inference guarantees. Our results are built based on the local conic geometry and duality. The difficulty of statistical inference is captured by the geometric characterization of the local tangent cone through the Gaussian width and Sudakov estimate.
The original and published work is available at: https://projecteuclid.org/euclid.aos/1467894707#abstract
Cai, T., Liang, T., & Rakhlin, A. (2016). Geometric Inference for General High-Dimensional Linear Inverse Problems. The Annals of Statistics, 44 (4), 1536-1563. http://dx.doi.org/10.1214/15-AOS1426
Date Posted: 27 November 2017
This document has been peer reviewed.