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A smoothed bootstrap test for independence based on mutual information

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  • Wu, Edmond H.C.
  • Yu, Philip L.H.
  • Li, W.K.

Abstract

A test for independence of multivariate time series based on the mutual information measure is proposed. First of all, a test for independence between two variables based on i.i.d. (time-independent) data is constructed and is then extended to incorporate higher dimensions and strictly stationary time series data. The smoothed bootstrap method is used to estimate the null distribution of mutual information. The experimental results reveal that the proposed smoothed bootstrap test performs better than the existing tests and can achieve high powers even for moderate dependence structures. Finally, the proposed test is applied to assess the actual independence of components obtained from independent component analysis (ICA).

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Bibliographic Info

Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 53 (2009)
Issue (Month): 7 (May)
Pages: 2524-2536

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Handle: RePEc:eee:csdana:v:53:y:2009:i:7:p:2524-2536

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  1. Shimizu, Shohei & Hyvarinen, Aapo & Hoyer, Patrik O. & Kano, Yutaka, 2006. "Finding a causal ordering via independent component analysis," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3278-3293, July.
  2. Kojadinovic, Ivan, 2004. "Agglomerative hierarchical clustering of continuous variables based on mutual information," Computational Statistics & Data Analysis, Elsevier, vol. 46(2), pages 269-294, June.
  3. La Rocca, Michele & Perna, Cira, 2005. "Variable selection in neural network regression models with dependent data: a subsampling approach," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 415-429, February.
  4. Zheng, John Xu, 2000. "A Consistent Test Of Conditional Parametric Distributions," Econometric Theory, Cambridge University Press, vol. 16(05), pages 667-691, October.
  5. Yongmiao Hong & Halbert White, 2005. "Asymptotic Distribution Theory for Nonparametric Entropy Measures of Serial Dependence," Econometrica, Econometric Society, vol. 73(3), pages 837-901, 05.
  6. Robinson, P M, 1991. "Consistent Nonparametric Entropy-Based Testing," Review of Economic Studies, Wiley Blackwell, vol. 58(3), pages 437-53, May.
  7. Ahmad, Ibrahim A. & Li, Qi, 1997. "Testing independence by nonparametric kernel method," Statistics & Probability Letters, Elsevier, vol. 34(2), pages 201-210, June.
  8. Taskinen, S. & Sirkia, S. & Oja, H., 2007. "Independent component analysis based on symmetrised scatter matrices," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 5103-5111, June.
  9. Meintanis, Simos G. & Iliopoulos, George, 2008. "Fourier methods for testing multivariate independence," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1884-1895, January.
  10. Buhlmann, Peter & Kunsch, Hans R., 1999. "Block length selection in the bootstrap for time series," Computational Statistics & Data Analysis, Elsevier, vol. 31(3), pages 295-310, September.
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