Adjustable Robust Singular Value Decomposition: Design, Analysis and Application to Finance
Abstract
:1. Introduction
1.1. Alternating Approach
1.2. The Effect of Noise on SVD
2. Robustness Analysis
2.1. Robustness Analysis for Different Estimators
2.2. The Selection of K
3. Adjustable Robust SVD Algorithms
3.1. Myriad Robust SVD (MySVD)
Algorithm 1 Calculate the first eigentriple |
Start with an initial guess of the leading left eigenvector and a constant value p |
repeat |
for each column j do |
end for |
for each row i do |
end for |
until Convergence |
3.2. Sequential MySVD
Algorithm 2 Sequential MySVD |
Known: |
Original data , new data |
Process: |
|
4. Application
4.1. Model Set Up
4.2. Factor Extraction
4.3. Numerical Example
5. Conclusion and Future Research
Acknowledgments
Conflicts of Interest
Appendix A. A Simulation Example
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Estimator | Cost Function | Output, |
---|---|---|
Linear | ||
Median | ||
Myriad |
Factors | Conventional SVD | Myriad Robust SVD (MySVD) |
---|---|---|
1 | ||
2 | ||
3 | ||
4 | ||
5 | ||
All Factors |
h-value | p-value | |||
---|---|---|---|---|
MySVD | 0 | |||
SVD | 1 |
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Wang, D. Adjustable Robust Singular Value Decomposition: Design, Analysis and Application to Finance. Data 2017, 2, 29. https://doi.org/10.3390/data2030029
Wang D. Adjustable Robust Singular Value Decomposition: Design, Analysis and Application to Finance. Data. 2017; 2(3):29. https://doi.org/10.3390/data2030029
Chicago/Turabian StyleWang, Deshen. 2017. "Adjustable Robust Singular Value Decomposition: Design, Analysis and Application to Finance" Data 2, no. 3: 29. https://doi.org/10.3390/data2030029