Publications

2018

1. ICAAMM

   Covariance matrix estimation of an ellipti- cally symmetric distributions in high dimensional setting

   F. Mezoued A. M. Haddouche

   In International Conference on Applied Analysis and Mathematical Modeling (ICAAMM) 2018

2020

1. JDS

   Scale matrix estimation under data-based loss in high and low dimensions

   F. Mezoued A. M. Haddouche

   In 52èmes Journées de Statistique de la Société Française de Statistique (SFdS) 2020

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   This paper deals with the problem of estimating the precision matrix for a scale mixture of Wishart distributions under Efron-Morris type losses tr(Σˆ−1 −Σ−12Sk), for k = 0, 1, 2 ..., where S is the sample covariance matrix. We derive orthogonally invariant estimators that dominate estimators of the form aS+, where a is a positive constant and S+ is the Moore Penrose inverse of S.

2021

1. JMVA

   Scale matrix estimation of an elliptically symmetric distribution in high and low dimensions

   Anis M. Haddouche, Dominique Fourdrinier, and Fatiha Mezoued

   Journal of Multivariate Analysis 2021

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   The problem of estimating the scale matrix Σ in a multivariate additive model, with elliptical noise, is considered from a decision-theoretic point of view. As the natural estimators of the form Σˆa=aS (where S is the sample covariance matrix and a is a positive constant) perform poorly, we propose estimators of the general form Σˆa,G=a(S+SS+G(Z,S)), where S+ is the Moore–Penrose inverse of S and G(Z,S) is a correction matrix. We provide conditions on G(Z,S) such that Σˆa,G improves over Σˆa under the quadratic loss L(Σ,Σˆ)=tr(ΣˆΣ−1−Ip)2. We adopt a unified approach to the two cases where S is invertible and S is singular. To this end, a new Stein–Haff type identity and calculus on eigenstructure for S are developed. Our theory is illustrated with a large class of estimators which are orthogonally invariant.

2. SPL

   Covariance matrix estimation under data-based loss

   Dominique Fourdrinier, Anis M. Haddouche, and Fatiha Mezoued

   Statistics & Probability Letters 2021

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   We consider here the problem of estimating the p×p scale matrix Σ of a multivariate linear regression model when the distribution of the observed matrix belongs to a large class of elliptically symmetric distributions. Any estimator Σˆ of Σ is assessed through the data-based loss tr(S+Σ(Σ−1Σˆ−Ip)2) where S is the sample covariance matrix and S+ is its Moore–Penrose inverse.

2022

1. CRM

   A unified approach for covariance matrix estimation under Stein loss

   Anis M. Haddouche, and Wei Lu

   Comptes Rendus. Mathématique 2022

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   In this paper, we address the problem of estimating a covariance matrix of a multivariate Gaussian distribution, from a decision theoretic point of view, relative to a Stein type loss function. We investigate the case where the covariance matrix is invertible and the case when it is non–invertible in a unified approach.

2. ECTEL

   Development of Actionable Insights for Regulating Students’ Collaborative Writing of Scientific Texts

   Christian Hoffmann, Nadine Mandran, Cédric d’Ham, and 2 more authors

   In Educating for a New Future: Making Sense of Technology-Enhanced Learning Adoption 2022

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   We develop indicators for teachers to monitor and regulate students’ collaborative writing on a web-based science learning environment. Visualiza- tions of carefully selected indicators are proposed to teachers in order to facilitate the tracking, analysis and management of the students’ collaborative work pro- cess over time. Our research method is based on a user-centered approach. Via focus groups and interviews, teachers have participated in the design of the indi- cators and visualizations. This communication presents (a) the mapping from col- lected data to educational constructs underlying our analytical approach for col- laborative writing, (b) indicators and visualizations produced to provide actiona- ble insights to teachers, and (c) lessons learned from our iterative human-centered design process. The results are transferable to other learning environments and design processes.

2023

1. CSEDU

   Proposal of Indicators for Measuring Collaborative Writing in a Digital Learning Environment

   Anis M. Haddouche., Fahima Djelil., Christian Hoffmann., and 2 more authors

   2023

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   Collaborative Writing (CW) is a common activity in education, which is being enhanced by the use of digital learning environments, leading to a growing research field in Computer-Supported Collaborative Learning (CSCL). In order to help teachers to monitor students CW, we propose two indicators that provide measures of student contributions to a text writing, namely balance of contribution and co-writing. We also identified CW strategies that are well defined in the literature. Moreover, we conducted a questionnaire evaluation to verify the interpretation of the indicators and the strategies by teachers in higher education context, using student reports edited in a collaborative digital environment called LabNbook, during physics and chemistry courses in undergraduate level. Results showed that teachers have a good interpretation of the indicators and strategies. This work contributes to research insights in CW, and motivates future work to design meaningful learning indicators.

2024

1. MMS

   Truncated Estimators for a Precision Matrix

   Anis M. Haddouche, and Dominique Fourdrinier

   Mathematical Methods of Statistics 2024

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   In this paper, we estimate the precision matrix Σ−1 of a Gaussian multivariate linear regressionmodelthroughitscanonicalform(ZT,UT)T where Z and U are respectively an m×p and an n × p matrices. This problem is addressed under the data-based loss function tr [(Σˆ −1 − Σ − 1 ) S ] 2, where Σˆ−1 estimates Σ− 1 , for any ordering of m, n and p, in a unified approach. We derive estimators which, besides the information contained in the sample covariance matrix S = U T U , use the information contained in the sample mean Z. We provide conditions for which these estimators improve over the usual estimators aS+ where a is a positive constant and S+ is the Moore-Penrose inverse of S. Thanks to the role of Z, such estimators are also improved by their truncated version.