An Alternative Definition of Finite-Sample Breakdown Point with Applications to Regression Model Estimators

1995 ◽  
Vol 90 (431) ◽  
pp. 1099-1106 ◽  
Author(s):  
Shinichi Sakata ◽  
Halbert White
Keyword(s):  
Regression Model ◽  
Breakdown Point ◽  
Finite Sample ◽  
Alternative Definition ◽  
Definition Of ◽  
Finite Sample Breakdown Point

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

scholarly journals Modal Principal Component Analysis

2020 ◽  
Vol 32 (10) ◽  
pp. 1901-1935
Author(s):  
Keishi Sando ◽  
Hideitsu Hino
Keyword(s):  
Principal Component Analysis ◽  
Minor Component ◽  
Principal Component ◽  
Breakdown Point ◽  
Component Analysis ◽  
Finite Sample ◽  
Robust Pca ◽  
Theoretical Contribution ◽  
Mode Estimation ◽  
Finite Sample Breakdown Point

Principal component analysis (PCA) is a widely used method for data processing, such as for dimension reduction and visualization. Standard PCA is known to be sensitive to outliers, and various robust PCA methods have been proposed. It has been shown that the robustness of many statistical methods can be improved using mode estimation instead of mean estimation, because mode estimation is not significantly affected by the presence of outliers. Thus, this study proposes a modal principal component analysis (MPCA), which is a robust PCA method based on mode estimation. The proposed method finds the minor component by estimating the mode of the projected data points. As a theoretical contribution, probabilistic convergence property, influence function, finite-sample breakdown point, and its lower bound for the proposed MPCA are derived. The experimental results show that the proposed method has advantages over conventional methods.

scholarly journals The finite sample breakdown point of PCS

2014 ◽  
Vol 94 ◽  
pp. 214-220 ◽  
Author(s):  
Eric Schmitt ◽  
Viktoria Öllerer ◽  
Kaveh Vakili
Keyword(s):  
Breakdown Point ◽  
Finite Sample ◽  
Finite Sample Breakdown Point
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