Asymptotic Properties of the Plug-in Estimator of the Discrete Entropy under Dependence

The Institute of Economics will hold a webinar meeting as part of its Seminar Series on Tuesday, February 9, 2021: Raffaello Seri from the Università degli Studi dell'Insubria will present the paper "Asymptotic Properties of the Plug-in Estimator of the Discrete Entropy under Dependence".

Abstract:

The authors consider the estimation of the entropy of a discretely-supported time series through a plug-in estimator. They provide a correction of the bias and we study the asymptotic properties of the estimator. The authors show that the widely-used correction proposed by Roulston (1999) is incorrect as it does not remove the O(1/N) part of the bias while ours does. They provide the asymptotic distribution and show that it differs when the values taken by the marginal distribution of the process are equiprobable (a situation that we call degeneracy) and when they are not. They also introduce estimators of the bias, the variance and the distribution under degeneracy and they study the estimation error. Finally, they propose a goodness-of-fit test based on entropy and give two motivations for it. The theoretical results are supported by specific numerical examples.

All interested participants are welcome to join online at the following link. External participants need to contact the organisers via email to grant access to the seminar.