The Influence of the Design on the Breakdown Point of ℓ1-type M-estimators

2001 ◽  
pp. 193-200 ◽  
Author(s):  
I. Mizera ◽  
Ch. H. Müller
Keyword(s):  
Breakdown Point

scholarly journals Breakdown and Evolution of the Protective Oxide Scales of AISI 304 and AISI 316 Stainless Steels under High-Temperature Oxidation

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
K. A. Habib ◽  
M. S. Damra ◽  
J. J. Saura ◽  
I. Cervera ◽  
J. Bellés
Keyword(s):  
Stainless Steel ◽  
Stainless Steels ◽  
Breakdown Point ◽  
304 Stainless Steel ◽  
Aisi 304 Stainless Steel ◽  
Protective Oxide ◽  
Aisi 304 ◽  
316 Stainless Steel ◽  
Aisi 316 Stainless Steel ◽  
Aisi 316

The failure of the protective oxide scales of AISI 304 and AISI 316 stainless steels has been studied and compared at 1,000°C in synthetic air. First, the isothermal thermogravimetric curves of both stainless steels were plotted to determine the time needed to reach the breakdown point. The different resistance of each stainless steel was interpreted on the basis of the nature of the crystalline phases formed, the morphology, and the surface structure as well as the cross-section structure of the oxidation products. The weight gain of AISI 304 stainless steel was about 8 times greater than that of AISI 316 stainless steel, and AISI 316 stainless steel reached the breakdown point about 40 times more slowly than AISI 304 stainless steel. In both stainless steels, reaching the breakdown point meant the loss of the protective oxide scale of Cr2O3, but whereas in AISI 304 stainless steel the Cr2O3scale totally disappeared and exclusively Fe2O3was formed, in AISI 316 stainless steel some Cr2O3persisted and Fe3O4was mainly formed, which means that AISI 316 stainless steel is more resistant to oxidation after the breakdown.

The Finite Sample Breakdown Point of \boldmath$\ell_1$-Regression

2004 ◽  
Vol 14 (4) ◽  
pp. 1028-1042 ◽  
Author(s):  
Avi Giloni ◽  
Manfred Padberg
Keyword(s):  
Breakdown Point ◽  
Finite Sample ◽  
Finite Sample Breakdown Point

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.

scholarly journals Breakdown Point of Robust Support Vector Machines

Entropy ◽  
2017 ◽  
Vol 19 (2) ◽  
pp. 83 ◽  
Author(s):  
Takafumi Kanamori ◽  
Shuhei Fujiwara ◽  
Akiko Takeda
Keyword(s):  
Support Vector Machines ◽  
Breakdown Point ◽  
Support Vector ◽  
Vector Machines

scholarly journals Finite sample breakdown point of Tukey’s halfspace median

2017 ◽  
Vol 60 (5) ◽  
pp. 861-874 ◽  
Author(s):  
XiaoHui Liu ◽  
YiJun Zuo ◽  
QiHua Wang
Keyword(s):  
Breakdown Point ◽  
Finite Sample ◽  
Finite Sample Breakdown Point
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