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

@article{Haddouche2020ScaleME, title={Scale matrix estimation under data-based loss in high and low dimensions}, author={Mohamed Anis Haddouche and Dominique Fourdrinier and Fatiha Mezoued}, journal={arXiv: Statistics Theory}, year={2020} }

We consider the problem of estimating the scale matrix $\Sigma$ of the additif model $Y_{p\times n} = M + \mathcal{E}$, under a theoretical decision point of view. Here, $ p $ is the number of variables, $ n$ is the number of observations, $ M $ is a matrix of unknown parameters with rank $q m$ (S non-invertible), we propose estimators of the form ${\hat{\Sigma}}_{a, G} = a\big( S+ S \, {S^{+}\,G(Z,S)}\big)$ where ${S^{+}}$ is the Moore-Penrose inverse of $ S$ (which coincides with $S^{-1… Expand

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