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Estimation of the parameters of a Wishart extension on symmetric matrices
Ghorbel Emna,Kammoun Kaouthar,Louati Mahdi,Sallem Akram 한국통계학회 2022 Journal of the Korean Statistical Society Vol.51 No.4
This paper deals with the parameters of a natural extension of the Wishart distribution, that is the Riesz distribution on the space of symmetric matrices. We estimate the shape parameter using two different approaches. The first one is based on the method of moments, we give its expression and investigate some of its properties. The second represents the maximum likelihood estimator. Unfortunately, in this case we do not have an explicit formula for this estimator. This latter is expressed in terms of the digamma function and sample mean of log-gamma variables. However, we derive the strong consistency and asymptotic normality properties of this estimator. A numerical comparative study between the two estimators is carried out in order to test the performance of the proposed approaches. For the second parameter, that is the scale parameter, we prove that the distribution of the maximum likelihood estimator given by Kammoun et al. (J Statist Prob Lett 126:127–131, 2017) is related to the Riesz distribution. We examine some properties concerning this estimator and we assess its performance by a numerical study.
A MUSIC-TYPE ALGORITHM FOR DETECTING INTERNAL CORROSION FROM ELECTROSTATIC BOUNDARY MEASUREMENTS
Habib AMMARI,Hyeon Bae KANG,EUN Joo KIM,Kaouthar LOUATI,Michael VOGELIUS 한국산업응용수학회 2006 한국산업응용수학회 학술대회 논문집 Vol.1 No.2
We establish an asymptotic representation formula for the steady state currents caused by internal corrosive parts of small Hausdorff measures. Based on this formula we design a non-iterative method of MUSIC (multiple signal classification) type for localizing the corrosive parts from voltage-to-current observations.