Collection Nexus Trimester - 2016 - Inference Problems Theme
Organizer(s)
Date(s)
27/04/2024
Testing temporal causality and estimating directed information
The problem of estimating the directed information rate between two Markov chains of arbitrary (but finite) order is considered. Specifically for the so-called “plug-in” (or maximum-likelihood) estimator, under natural conditions we show that it is consistent with probability one, and that it is asymptotically Gaussian. From this it is show that its convergence rate is of O(1/n√), which is the best possible. A connection is established between this estimation problem and that of performing a hypothesis test for the presence of causal influence between the two processes. Under the null hypothesis, which corresponds to the absence of (temporal) causality, we show that the plug-in estimator has an asymptotic χ2distribution, and that this estimator can be expressed precisely in terms of the classical likelihood ratio statistic. Combining these two results facilitates the design of a Neyman-Pearson likelihood ratio test for the presence of causal influence. This is joint work with Maria Skoularidou.
