The Preliminary Results on Super Robustness
Abstract
In this paper, we investigate super robust estimation approaches, which generate a reliable estimation even when the noise observations are more than half in an experiment. The following preliminary research results on super robustness are presented: (1) It is proved that statistically, the maximum likelihood location estimator of exponential power distribution (or L^p location estimator, for short) is strict super robust, for a given p<1. (2) For a given experiment and a super robust estimator family, there is an estimator that generates an estimation that is close enough to a perfect estimation, for general transformation groups. (3)L^p estimator family is a super robust estimator family. (4) For a given experiment, L^p estimator on translation, scaling and rotation generates perfect estimation when p is small enough, even for very noisy experiments.
Cite
@article{arxiv.1208.1810,
title = {The Preliminary Results on Super Robustness},
author = {Qinghuai Gao},
journal= {arXiv preprint arXiv:1208.1810},
year = {2015}
}
Comments
v4, differentiate with compressive sensing; v5, did minor fix and changed to small fonts; v6, the first effort on general transformation is added; v7, improve the algorithm in the section 4.2; v8,remove Remark; v9, add section 4.3; v10, new title, abstract, and 4.3/4.4; v11, Theorem 7. v12, remove 4.2; v14: ebbing algorithm; arXiv admin note: text overlap with arXiv:1206.5057