Generalized entropy-based criterion for consistent testing

Through the use of a recently introduced, nonextensive, entropy, we generalize that of Kullback and Leibler [Ann. Math. Stat. 22, 79 (1961)] and study its properties. This in turn enables the proposal of a consistent criterion for testing relevant hypotheses such as the independence of random variables. Straightforward applications are shown to be possible for (physical, geophysical, economic, and biological) time series.