A highly robust estimator for regression models

Abstract

It is well known that classical robust estimators tolerate only less than fifty percent of outliers. However, situations with more than fifty percent of outliers often occur in practice. The efficient identification of objects from a noisier background is thus a difficult problem. In this paper, a highly robust estimator is formulated to tackle such a difficulty. The proposed estimator is called the regression density decomposition (RDD) estimator. The computational analysis of the estimator and its properties are discussed and a simulated annealing algorithm is proposed for its implementation. It is demonstrated that the RDD estimator can resist a very large proportion of noisy data, even more than fifty percent. It is successfully applied to some simulated and real-life noisy data sets. It appears that the estimator can solve efficiently and effectively general regression problems, pattern recognition, computer vision and data mining problems.