Improved Measures of Kurtosis And Their Application in ICA
With comparison of the classical kurtosis measures and its application in ICA
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Kurtosis plays important role in defining shape characteristics of a probability distribution, and also in extracting as well as sorting independent components. From recent research on various versions of classical kurtosis we see that all the measures substantially underestimate kurtosis parameter and exhibit high variability when underlying population distribution is highly skewed or heavy tailed. This is unwanted for ICA. In this book, we propose a bootstrap bias corrected estimator and compare it with the version of classical measure that is found best in recent works. We use both simulate...
Kurtosis plays important role in defining shape characteristics of a probability distribution, and also in extracting as well as sorting independent components. From recent research on various versions of classical kurtosis we see that all the measures substantially underestimate kurtosis parameter and exhibit high variability when underlying population distribution is highly skewed or heavy tailed. This is unwanted for ICA. In this book, we propose a bootstrap bias corrected estimator and compare it with the version of classical measure that is found best in recent works. We use both simulated and real data. Our proposed estimator performs better in the both cases. We then apply our measure in sorting independent components in two data sets and try to examine the capacity of PCA, ICA and ICA on PCA for finding groups. In both data sets ICA on PCA shows the maximum discriminating power whereas PCA the least. We recommend using our proposed measure in both extracting and sorting independent components.
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