Abstract
Robust regression is an important iterative procedure that seeks analyzing data sets that are contaminated with outliers and unusual observations and reducing their impact over regression coefficients. Robust estimation methods have been introduced to deal with the problem of outliers and provide efficient and stable estimates in their presence. Various robust estimators have been developed in the literature to restrict the unbounded influence of the outliers or leverage points on the model estimates. Here, a new redescending M-estimator is proposed using a novel objective function with the prime focus on getting highly robust and efficient estimates that give promising results. It is evident from the results that, for normal and clean data, the proposed estimator is almost as efficient as ordinary least square method and, however, becomes highly resistant to outliers when it is used for contaminated datasets. The simulation study is being carried out to assess the performance of the proposed redescending M-estimator over different data generation scenarios including normal, t-distribution, and double exponential distributions with different levels of outliers’ contamination, and the results are compared with the existing redescending M-estimators, e.g., Huber, Tukey Biweight, Hampel, and Andrew-Sign function. The performance of the proposed estimators was also checked using real-life data applications of the estimators and found that the proposed estimators give promising results as compared to the existing estimators.
Highlights
Robust regression is an alternative method to the ordinary least square (OLS) regression when the basic assumptions are violated by the nature of the data. e method of OLS requires several assumptions to fit a regression line efficiently, but it produces very poor estimates of the regression coefficients when the same assumptions are not fulfilled, and the residuals become very large leading to inflated standard errors, which can seriously distort model predictions. us, the confidence interval becomes wider, and the estimates of the regression coefficients are no longer asymptotically consistent
During estimation of the regression coefficients, if assumptions of the OLS are violated, this problem is often fixed by using the transformation techniques. e transformed variables sometimes eliminate the effect of the influential outliers, which can affect the significance of the regression coefficients that can lead to incorrect predictions
Keeping in view the weaker performance of the available robust estimators, an attempt has been made in this paper to introduce a novel redescending M-estimator that outperforms the existing robust methods in terms of efficiency and robustness, which gives promising results. e main contribution in this paper is to propose a new redescending M-estimator that has the potential to perform well in almost all kinds of contaminated datasets without compromising on its efficiency
Summary
Robust regression is an alternative method to the ordinary least square (OLS) regression when the basic assumptions are violated by the nature of the data. e method of OLS requires several assumptions to fit a regression line efficiently, but it produces very poor estimates of the regression coefficients when the same assumptions are not fulfilled, and the residuals become very large leading to inflated standard errors, which can seriously distort model predictions. us, the confidence interval becomes wider, and the estimates of the regression coefficients are no longer asymptotically consistent. E transformed variables sometimes eliminate the effect of the influential outliers, which can affect the significance of the regression coefficients that can lead to incorrect predictions. Under these situations, robust regression methods that are resistant to outliers become the only best choice left to fit the regression line and find efficient estimates of the regression coefficients. I 1 where ei yi − xTi β represents the vectors of residuals This estimator is very sensitive to bad observations and to even a small departure of the data points from normality. Keeping in view the weaker performance of the available robust estimators, an attempt has been made in this paper to introduce a novel redescending M-estimator that outperforms the existing robust methods in terms of efficiency and robustness, which gives promising results. e main contribution in this paper is to propose a new redescending M-estimator that has the potential to perform well in almost all kinds of contaminated datasets without compromising on its efficiency
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
