A Lower Bound on the Estimator Variance for the Sparse Linear Model
Statistics Theory
2010-09-20 v1 Information Theory
math.IT
Statistics Theory
Abstract
We study the performance of estimators of a sparse nonrandom vector based on an observation which is linearly transformed and corrupted by additive white Gaussian noise. Using the reproducing kernel Hilbert space framework, we derive a new lower bound on the estimator variance for a given differentiable bias function (including the unbiased case) and an almost arbitrary transformation matrix (including the underdetermined case considered in compressed sensing theory). For the special case of a sparse vector corrupted by white Gaussian noise-i.e., without a linear transformation-and unbiased estimation, our lower bound improves on previously proposed bounds.
Cite
@article{arxiv.1009.3353,
title = {A Lower Bound on the Estimator Variance for the Sparse Linear Model},
author = {Sebastian Schmutzhard and Alexander Jung and Franz Hlawatsch and Zvika Ben-Haim and Yonina C. Eldar},
journal= {arXiv preprint arXiv:1009.3353},
year = {2010}
}