A high breakdown, high efficiency and bounded influence modified GM estimator based on support vector regression

ABSTRACT

Regression analysis aims to estimate the approximate relationship between the response variable and the explanatory variables. This can be done using classical methods such as ordinary least squares. Unfortunately, these methods are very sensitive to anomalous points, often called outliers, in the data set. The main contribution of this article is to propose a new version of the Generalized M-estimator that provides good resistance against vertical outliers and bad leverage points. The advantage of this method over the existing methods is that it does not minimize the weight of the good leverage points, and this increases the efficiency of this estimator. To achieve this goal, the fixed parameters support vector regression technique is used to identify and minimize the weight of outliers and bad leverage points. The effectiveness of the proposed estimator is investigated using real and simulated data sets.

KEYWORDS:

• Robust regression
• breakdown point
• outliers
• leverage points
• support vector regression

Acknowledgments

We are grateful to the reviewers for their valuable comments and suggestions which have improved the article.

Disclosure statement

No potential conflict of interest was reported by the authors.