The Preliminary Results on Super Robustness

TL;DR

This paper explores super robust estimation methods capable of providing reliable results even when noise observations exceed half of the data, introducing theoretical proofs and specific estimator families demonstrating this robustness.

Contribution

It proves the super robustness of L^p estimators for p<1 and shows their effectiveness under various transformations and noise conditions.

Findings

L^p estimators are strictly super robust for p<1.

Super robust estimators can achieve near-perfect estimation despite high noise.

L^p estimators perform well under translation, scaling, and rotation transformations.

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.