Statistics Papers

Document Type

Journal Article

Date of this Version

7-2016

Publication Source

The Annals of Statistics

Volume

44

Issue

4

Start Page

1536

Last Page

1563

DOI

10.1214/15-AOS1426

Abstract

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.

Copyright/Permission Statement

The original and published work is available at: https://projecteuclid.org/euclid.aos/1467894707#abstract

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Date Posted: 27 November 2017

This document has been peer reviewed.