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Bounds for the estimation of matrix-valued parameters of a Gaussian random process

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Title: Bounds for the estimation of matrix-valued parameters of a Gaussian random process
Authors: Leon Arencibia, Lorena, Wendt, Herwig, Tourneret, Jean-Yves
Contributors: CoMputational imagINg anD viSion (IRIT-MINDS), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Institut National Polytechnique (Toulouse) (Toulouse INP), Centre National de la Recherche Scientifique (CNRS), ANR-18-CE45-0007,MUTATION,Analyse multifractale multidimensionnelle : Théorie et applications en imagerie échographique du cancer de pancréas(2018)
Source: ISSN: 0165-1684.
Publisher Information: CCSD
Elsevier
Publication Year: 2023
Collection: Université Toulouse III - Paul Sabatier: HAL-UPS
Subject Terms: Bayesian Cramér-Rao lower bound, Wishart random matrices, Multivariate multifractal analysis, [INFO]Computer Science [cs]
Description: International audience ; This paper derives and studies Bayesian Cramér-Rao lower bounds for the mean squared error of covariance matrices that are structured as weighted sums of symmetric positive definite matrices associated with a circularly-symmetric Gaussian statistical model. This model naturally appears in a number of important applications, including multivariate multifractal analysis and vector-valued additive Gaussian processes. As an intermediary result, we derive a novel expression for the expectation of compositions of Wishart random matrices. We provide extensive numerical simulation results for analyzing the derived bounds and their properties, and illustrate their use for the multifractal analysis of bivariate time series.
Document Type: article in journal/newspaper
Language: English
DOI: 10.1016/j.sigpro.2023.109106
Availability: https://hal.science/hal-04254235
https://hal.science/hal-04254235v1/document
https://hal.science/hal-04254235v1/file/1-s2.0-S0165168423001809-main.pdf
https://doi.org/10.1016/j.sigpro.2023.109106
Rights: http://creativecommons.org/licenses/by/ ; info:eu-repo/semantics/OpenAccess
Accession Number: edsbas.4ADF4FB0
Database: BASE
Description
Abstract:International audience ; This paper derives and studies Bayesian Cramér-Rao lower bounds for the mean squared error of covariance matrices that are structured as weighted sums of symmetric positive definite matrices associated with a circularly-symmetric Gaussian statistical model. This model naturally appears in a number of important applications, including multivariate multifractal analysis and vector-valued additive Gaussian processes. As an intermediary result, we derive a novel expression for the expectation of compositions of Wishart random matrices. We provide extensive numerical simulation results for analyzing the derived bounds and their properties, and illustrate their use for the multifractal analysis of bivariate time series.
DOI:10.1016/j.sigpro.2023.109106