On the Finite-Sample Analysis of $\Theta$-estimators
Statistics Theory
2016-10-11 v3 Statistics Theory
Abstract
In large-scale modern data analysis, first-order optimization methods are usually favored to obtain sparse estimators in high dimensions. This paper performs theoretical analysis of a class of iterative thresholding based estimators defined in this way. Oracle inequalities are built to show the nearly minimax rate optimality of such estimators under a new type of regularity conditions. Moreover, the sequence of iterates is found to be able to approach the statistical truth within the best statistical accuracy geometrically fast. Our results also reveal different benefits brought by convex and nonconvex types of shrinkage.
Keywords
Cite
@article{arxiv.1512.03987,
title = {On the Finite-Sample Analysis of $\Theta$-estimators},
author = {Yiyuan She},
journal= {arXiv preprint arXiv:1512.03987},
year = {2016}
}