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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