Statistical Independence, Measures and Testing
Yaseen Unnisa, D. Tran, Fu Chun Huang · 2013
Independent Component Analysis has recently been employed in structural damage detection and blind source separation to extract source signals and the unmixing matrix of the system from response signals. This novel method relies on the assumption that source signals are statistically independent. This paper looks at statistical independence, its measures and testing procedures. First the concepts of kurtosis, negentropy and mutual information are reviewed, followed by Bakirov’s measures of coefficient of statistical independence and distance correlation between two signals coupled with Hypothesis testing to avoid Type I and Type II error. Bakirov’s tests are nonparametric, simple to implement and do not require any approximation. Algorithms developed by Bakirov and associates to test the statistical independence of two arbitrary signals are reviewed. A case study using signals commonly found in vibration testing showed that Bakirov’s tests are both reliable and rigorous. They are then applied to investigate the effects of corrupted signals by various forms on the statistical independence and performance of fastICA, a popular independent component analysis algorithm.