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Title: Entropy based tests of dependence for categorical data Authors:  Simone Giannerini - University of Bologna (Italy) [presenting]
Greta Goracci - University of Bologna (Italy)
Abstract: The literature on measures of dependence and on tests for independence for categorical data is very wide. We focus on the power-divergence family of statistics, that includes as a special case both the measure $S_{\rho}$ and Pearson's chi square. Nevertheless, the theoretical derivations concern the null hypothesis of stochastic independence against the alternative of some sort of local deviation from it. We derive an asymptotic approximation valid for the whole family and for every given level of dependence. This allows to build tests where $H_0:S_{\rho} = S_0 \geq 0$ against $H_1: S_{\rho} \neq S_0$. Moreover, we can compute analytically the power of the tests for independence that rely on the power-divergence family. We compare the performance of tests based on $S_{\rho}$ with that of classical $\chi^2$ both analytically and by means of Monte Carlo studies.