arXiv 6 May 2019 · Statistics — Applications
arXiv:1905.02061 · PDF · DOI · OpenAlex · Extracted main text
In dealing with high-dimensional data, factor models are often used for reducing dimensions and extracting relevant information. The spectrum of covariance matrices from power data exhibits two aspects: 1) bulk, which arises from random noise or fluctuations and 2) spikes, which represents factors caused by anomaly events. In this paper, we propose a new approach to the estimation of high-dimensional factor models, minimizing the distance between the empirical spectral density (ESD) of covariance matrices of the residuals of power data that are obtained by subtracting principal components and the limiting spectral density (LSD) from a multiplicative covariance structure model. The free probability theory (FPT) is used to derive the spectral density of the multiplicative covariance model, which efficiently solves the computational difficulties. The proposed approach connects the estimation of the number of factors to the LSD of covariance matrices of the residuals, which provides estimators of the number of factors and the correlation structure information in the residuals. Considering a lot of measurement noise is contained in the power data and the correlation structure is complex for the residuals, the approach prefers approaching the ESD of covariance matrices of the residuals through a multiplicative covariance model, which avoids making crude assumptions or simplifications on the complex structure of the data. Theoretical studies show the proposed approach is robust against noise and sensitive to the presence of weak factors. The synthetic data from IEEE 118-bus power system is used to validate the effectiveness of the approach. Furthermore, the application to the analysis of the real-world online monitoring data in a power grid shows that the estimators in the approach can be used to indicate the system behavior.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | J. Yeo and G. Papanicolaou, “Random matrix approach to estimation of… (2016) Random matrix approach to estimation of high-dimensional factor models | 0.928 | 4 | 3 | 100% |
| 2 | J. Bai and S. Ng, “Determining the number of factors in approximate… (2002) Determining the number of factors in approximate factor models | 0.737 | 3 | 2 | 100% |
| 3 | A. Onatski, “Determining the number of factors from empirical distri… (2010) Determining the number of factors from empirical distribution of eigenvalues | 0.737 | 3 | 2 | 100% |
| 4 | J. H. Stock and M. W. Watson, “Forecasting using principal component… (2002) Forecasting using principal components from a large number of predictors | 0.644 | 2 | 2 | 100% |
| Shanghai 200240 | unmatched citation key Shanghai 200240 | 0.511 | 2 | 1 | 100% |
| Shanghai Jiao Tong University | unmatched citation key Shanghai Jiao Tong University | 0.511 | 2 | 1 | 100% |
| 7 | S. C. Ahn and A. R. Horenstein, “Eigenvalue ratio test for the numbe… (2013) Eigenvalue ratio test for the number of factors | 0.511 | 2 | 1 | 100% |
| China. E-mail: [email removed] | unmatched citation key China. E-mail: [email removed] | 0.405 | 1 | 1 | 100% |
| China.\protect\\ E-mail: [email removed] \IEEEcompsocthank… | unmatched citation key China.\protect\\ E-mail: [email removed] \IEEEcompsocthank… | 0.405 | 1 | 1 | 100% |
| 10 | IIT, “Index of data illinois institute of technology,” Illinois Inst… Index of data illinois institute of technology | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 25 scored citations. 4 of these could not be matched to a bibliography entry, so only the citation key is shown.