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

Autor:	Raffaello Seri, Mario Martinoli
Rok vydání:	2021
Předmět:	Entropy (classical thermodynamics) Series (mathematics) Estimator Applied mathematics Asymptotic distribution Library and Information Sciences Marginal distribution Information theory Degeneracy (mathematics) Random variable Computer Science Applications Information Systems Mathematics
Zdroj:	IEEE Transactions on Information Theory. 67:7659-7683
ISSN:	1557-9654 0018-9448
DOI:	10.1109/tit.2021.3109307
Popis:	We consider the estimation of the entropy of a discretely-supported time series through a plug-in estimator. We provide a correction of the bias and we study the asymptotic properties of the estimator. We show that the widely-used correction proposed by Roulston (1999) is incorrect as it does not remove the $O\left ({N^{-1}}\right)$ part of the bias while ours does. We provide the asymptotic distribution and we 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. We introduce estimators of the bias, the variance and the distribution under degeneracy and we study the estimation error. Finally, we propose a goodness-of-fit test based on entropy and give two motivations for it. The theoretical results are supported by specific numerical examples.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::7cd88bd13ded5571f2b92e35729b72de https://doi.org/10.1109/tit.2021.3109307 Zobrazit plný text záznamu