Abstract: We introduce a new class of measures that test for independence between two random vectors using the expected difference between conditional and marginal characteristic functions. Based on a selected weight function in the class, we propose a new index for measuring independence and study its properties. To illustrate the use of such an index, two empirical versions are developed: slicing and kernel approaches. Their asymptotic properties and applications are discussed. Lastly, simulation results demostrate the advantages of the proposed method.

Key words and phrases: Categorical variable, distance, independence.