An Intercomparison of Rules for Testing the Significance of Coupled Modes of Singular Value Decomposition Analysis

ZENG Qingcun

doi:10.1007/s00376-007-0199-2

Impact Factor: 5.8

Volume 24 Issue 2

Mar. 2007

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Article > ADVANCES IN ATMOSPHERIC SCIENCES > 2007 > 24(2): 199-212

An Intercomparison of Rules for Testing the Significance of Coupled Modes of Singular Value Decomposition Analysis

ZENG Qingcun

1.
Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing

ZENG Qingcun

doi: 10.1007/s00376-007-0199-2

Abstract
References
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Abstract:
This paper clarifies the essence of the significance test of singular value decomposition analysis (SVD), and investigates four rules for testing the significance of coupled modes of SVD, including parallel analysis, nonparametric bootstrap, random-phase test, and a new rule named modified parallel analysis. A numerical experiment is conducted to quantitatively compare the performance of the four rules in judging whether a coupled mode of SVD is significant as parameters such as the sample size, the number of grid points, and the signal-to-noise ratio vary. The results show that the four rules perform better with lower ratio of the number of grid points to sample size. Modified parallel analysis and nonparametric bootstrap perform best to abandon the spurious coupled modes, but the latter is better than the former to retain the significant coupled modes when the sample size is not much larger than the number of grid points. Parallel analysis and random-phase test are robust to abandon the spurious coupled modes only when either (1) the observations at the grid points are spatially uncorrelated, or (2) the coupled signal is very strong for parallel analysis and is not weak for random-phase test. The reasons affecting the accuracy of the test rules are discussed.
- singular value decomposition analysis,
- significance test
References

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Manuscript History

Manuscript received: 10 March 2007

Manuscript revised: 10 March 2007

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

An Intercomparison of Rules for Testing the Significance of Coupled Modes of Singular Value Decomposition Analysis

ZENG Qingcun

1. Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing

Manuscript received: 2007-03-10
Manuscript revised: 2007-03-10

Abstract: This paper clarifies the essence of the significance test of singular value decomposition analysis (SVD), and investigates four rules for testing the significance of coupled modes of SVD, including parallel analysis, nonparametric bootstrap, random-phase test, and a new rule named modified parallel analysis. A numerical experiment is conducted to quantitatively compare the performance of the four rules in judging whether a coupled mode of SVD is significant as parameters such as the sample size, the number of grid points, and the signal-to-noise ratio vary. The results show that the four rules perform better with lower ratio of the number of grid points to sample size. Modified parallel analysis and nonparametric bootstrap perform best to abandon the spurious coupled modes, but the latter is better than the former to retain the significant coupled modes when the sample size is not much larger than the number of grid points. Parallel analysis and random-phase test are robust to abandon the spurious coupled modes only when either (1) the observations at the grid points are spatially uncorrelated, or (2) the coupled signal is very strong for parallel analysis and is not weak for random-phase test. The reasons affecting the accuracy of the test rules are discussed.

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