Consistency results and confidence intervals for adaptive l1-penalized estimators of the high-dimensional sparse precision matrix

This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Avanesov, ValeriyPolzehl, JörgTabelow, Karsten2016-12-132019-06-2820162198-5855https://doi.org/10.34657/2143https://oa.tib.eu/renate/handle/123456789/1645In this paper we consider the adaptive '1-penalized estimators for the precision matrix in a finite-sample setting. We show consistency results and construct confidence intervals for the elements of the true precision matrix. Additionally, we analyze the bias of these confidence intervals. We apply the estimator to the estimation of functional connectivity networks in functional Magnetic Resonance data and elaborate the theoretical results in extensive simulation experiments.application/pdfeng510Adaptive l1 penaltyprecision matrixhigh-dimensional statisticssparsityconfidence intervalsfunctional connectivityConsistency results and confidence intervals for adaptive l1-penalized estimators of the high-dimensional sparse precision matrixReport