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Measures of dependence
 Matoušková, Monika ; Pawlas, Zbyněk (advisor) ; Dvořák, Jiří (referee)
The most common measure of dependence is the correlation coefficient. Its problem is that it can be zero for two dependent random variables. We will discuss two measures of dependence, which are equal to zero if and only if the two random variables are inde- pendent. We will compare them with Pearson's correlation coefficient. The first one will be the maximal correlation, which is often difficult to calculate. That is why we define the maximal polynomial correlation, which is easier to calculate and is non-decreasing in a degree of a polynomial. We also define the distance correlation and we discuss other ways of the expression of distance correlation, which can be used in the calculation. We deal with the case of normal distribution and we show some calculations of these measures of dependence. 1
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