Significance testing of information theoretic functionals

A transformation is derived, such that, under the transformation the mutual information of two unrelated variables is a normally distributed random variable with zero mean and unit variance. It is demonstrated that the transformed mutual information can be used as a test statistic to test the statistical significance of the relationship between variables and provides an alternative to the method of surrogate data. If the mutual information is regarded as a generalization of the linear correlation coefficient then this test statistic can be regarded as analogous to the Fisher-Z test statistic.