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Analysis of Multivariate and High-Dimensional Data by Inge Koch

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Problems for Part III

Independent Component Analysis

1.Give a proof of Theorem 10.2 with emphasis on the form of the matrix E. Hint: You may use the proof of Comon (1994).

2.Consider Fisher’s iris data. Leave out the ‘red’ species Setosa, and repeat the analyses of Example 10.2 for the remaining two species. Compare the results of the new analysis with those of Example 10.2.

3.Give a detailed proof of Proposition 10.8 stating precisely which results are used and how.

4.Explain why it is advantageous to sphere a random vector before finding the independent components but not prior to a Principal Component Analysis. Illustrate with the Swiss bank notes data.

5.Let X and Y be d-dimensional random vectors with probability density functions f and ...

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