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Open AccessArticle

Robust Regression with Density Power Divergence: Theory, Comparisons, and Data Analysis

1
Dipartimento di Scienze Economiche e Aziendale and Interdepartmental Centre for Robust Statistics, Università di Parma, l43125 Parma, Italy
2
The London School of Economics, London WC2A 2AE, UK
3
European Commission, Joint Research Centre, 21027 Ispra, Italy
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(4), 399; https://doi.org/10.3390/e22040399
Received: 22 February 2020 / Revised: 26 March 2020 / Accepted: 26 March 2020 / Published: 31 March 2020
Minimum density power divergence estimation provides a general framework for robust statistics, depending on a parameter α , which determines the robustness properties of the method. The usual estimation method is numerical minimization of the power divergence. The paper considers the special case of linear regression. We developed an alternative estimation procedure using the methods of S-estimation. The rho function so obtained is proportional to one minus a suitably scaled normal density raised to the power α . We used the theory of S-estimation to determine the asymptotic efficiency and breakdown point for this new form of S-estimation. Two sets of comparisons were made. In one, S power divergence is compared with other S-estimators using four distinct rho functions. Plots of efficiency against breakdown point show that the properties of S power divergence are close to those of Tukey’s biweight. The second set of comparisons is between S power divergence estimation and numerical minimization. Monitoring these two procedures in terms of breakdown point shows that the numerical minimization yields a procedure with larger robust residuals and a lower empirical breakdown point, thus providing an estimate of α leading to more efficient parameter estimates. View Full-Text
Keywords: estimation of α; monitoring; numerical minimization; S-estimation; Tukey’s biweight estimation of α; monitoring; numerical minimization; S-estimation; Tukey’s biweight
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Riani, M.; Atkinson, A.C.; Corbellini, A.; Perrotta, D. Robust Regression with Density Power Divergence: Theory, Comparisons, and Data Analysis. Entropy 2020, 22, 399.

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