  Information value (IV) is a quite popular technique for features selection
before the modeling phase. There are practical criteria, based on fixed
thresholds for IV, but at the same time mysterious and lacking theoretical
arguments, to decide if a predictor has sufficient predictive power to be
considered in the modeling phase. However, the mathematical development and
statistical inference methods for this technique are almost nonexistent in the
literature. In this paper we present a theoretical framework for IV, and at the
same time, we propose a non-parametric hypothesis test to evaluate the
predictive power of features contemplated in a data set. Due to its
relationship with divergence measures developed in the Information Theory, we
call our proposal the J - Divergence test. We show how to efficiently compute
our test statistic and we study its performance on simulated data. In various
scenarios, particularly in unbalanced data sets, we show its superiority over
conventional criteria based on fixed thresholds. Furthermore, we apply our test
on fraud identification data and provide an open-source Python library, called
"statistical-iv"(https://pypi.org/project/statistical-iv/), where we implement
our main results.
