Anis M. HADDOUCHE

Research Engineer

IMT Atlantique, LABSTICC

Brest, France

Hello and welcome to my website which is a tentative to gather my teaching and research activities.

I am a PhD on applied mathematics with a specialization in statistics. My research interests include decision theory, shrinkage estimators and multivariate statistics.

Currently, I am a research engineer at the LABSTICC laboratory within the MOTEL team since September 2021. I am also a freelance mentor on the Openclassrooms data training paths (Data Science, Data Analyst and Machine Learning Engineer).

From 2019 to 2021 I was a temporary teaching and research assistant (ATER) at INSA de Rouen Normandie.

selected publications

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.
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.