The Density Power Divergence

2011 ◽  
pp. 317-346
Keyword(s):  
Density Power Divergence ◽  
Power Divergence

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

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 399 ◽  
Author(s):  
Marco Riani ◽  
Anthony C. Atkinson ◽  
Aldo Corbellini ◽  
Domenico Perrotta
Keyword(s):  
Robust Regression ◽  
Robust Statistics ◽  
Estimation Method ◽  
Estimation Procedure ◽  
Breakdown Point ◽  
Parameter Estimates ◽  
Normal Density ◽  
Density Power Divergence ◽  
Numerical Minimization ◽  
Power Divergence

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.

Minimum density power divergence estimator for GARCH models

Test ◽  
2008 ◽  
Vol 18 (2) ◽  
pp. 316-341 ◽  
Author(s):  
Sangyeol Lee ◽  
Junmo Song
Keyword(s):  
Garch Models ◽  
Density Power Divergence ◽  
Minimum Density ◽  
Power Divergence

The power divergence and the density power divergence families: the mathematical connection

Sankhya B ◽  
2013 ◽  
Vol 75 (1) ◽  
pp. 16-28 ◽  
Author(s):  
Sujayendu Patra ◽  
Avijit Maji ◽  
Ayanendranath Basu ◽  
Leandro Pardo
Keyword(s):  
Density Power Divergence ◽  
Power Divergence ◽  
Mathematical Connection

scholarly journals Robust tests for the equality of two normal means based on the density power divergence

Metrika ◽  
2014 ◽  
Vol 78 (5) ◽  
pp. 611-634 ◽  
Author(s):  
A. Basu ◽  
A. Mandal ◽  
N. Martin ◽  
L. Pardo
Keyword(s):  
Density Power Divergence ◽  
Normal Means ◽  
Robust Tests ◽  
Power Divergence
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