H. M. Markowitz, Portfolio selection, Journal of Finance, vol.7, issue.1, pp.77-91, 1952.

R. Clarke, H. D. Silva, and S. Thorley, Minimum variance, maximum diversification, and risk parity: an analytic perspective, Journal of Portfolio Management, 2012.

S. Maillard, T. Roncalli, and J. Teiletche, The properties of equally weighted risk contributions portfolios, Journal of Portfolio Management, vol.36, pp.60-70, 2010.

Y. Choueifaty and Y. Coignard, Toward maximum diversification, Journal of Portfolio Management, vol.35, issue.1, pp.40-51, 2008.

Y. Choueifaty, T. Froidure, and J. Reynier, Properties of the most diversified portfolio, Journal of investment strategies, vol.2, issue.2, pp.49-70, 2013.

D. E. Tyler, A distribution-free M-estimator of multivariate scatter, The annals of Statistics, vol.15, issue.1, pp.234-251, 1987.

R. A. Maronna, Robust M-estimators of multivariate location and scatter, Annals of Statistics, vol.4, issue.1, pp.51-67, 1976.

Y. Chen, A. Wiesel, and A. O. Hero, Robust shrinkage estimation of high-dimensional covariance matrices, IEEE Transactions on Signal Processing, vol.59, issue.9, 2011.

F. Pascal, Y. Chitour, and Y. Quek, Generalized robust shrinkage estimator and its application to STAP detection problem, IEEE Transactions on Signal Processing, vol.62, issue.21, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01104004

Y. Abramovich and N. K. Spencer, Diagonally loaded normalised sample matrix inversion (LNSMI) for outlier-resistant adaptive filtering, IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP), vol.3, 2007.

O. Ledoit and M. Wolf, A well-conditioned estimator for largedimensional covariance matrices, Journal of Multivariate Analysis, vol.88, pp.365-411, 2004.

R. Couillet, F. Pascal, and J. W. Silverstein, Robust estimates of covariance matrices in the large dimensional regime, IEEE Transactions on Information Theory, vol.60, issue.11, 2014.

L. Yang, R. Couillet, and M. R. Mckay, A robust statistics approach to minimum variance portfolio optimization, IEEE Transactions on Signal Processing, vol.63, issue.24, pp.6684-6697, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01262628

W. F. Sharpe, Capital asset prices: A theory of market equilibrium under conditions of risk, Journal of Finance, vol.19, issue.3, pp.425-442, 1964.

, Max Variety -SCM Max Variety -RMT Tyler whitened Benchmark Fig. 2. All portfolios (MaxVariety) From Replicated Single Strategies

G. Schwarz, Estimating the dimension of a model, The Annals of Statistics, vol.6, issue.2, pp.461-464, 1978.

F. Pascal, Y. Chitour, J. P. Ovarlez, P. Forster, and P. Larzabal, Covariance structure maximum-likelihood estimates in compound Gaussian noise: Existence and algorithm analysis, IEEE Transactions on Signal Processing, vol.56, issue.1, pp.34-48, 2008.
URL : https://hal.archives-ouvertes.fr/hal-01816367

F. Pascal, P. Forster, J. P. Ovarlez, and P. Larzabal, Performance analysis of covariance matrix estimates in impulsive noise, IEEE Transactions on Signal Processing, vol.56, issue.6, pp.2206-2217, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00353591

M. Mahot, F. Pascal, P. Forster, and J. P. Ovarlez, Asymptotic properties of robust complex covariance matrix estimates, IEEE Transactions on Signal Processing, vol.61, issue.13, pp.3348-3356, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01705126

R. Couillet and M. Debbah, Random matrix methods for wireless communications, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00658725

S. Kritchman and B. Nadler, Non-parametric detection of the number of signals: Hypothesis testing and random matrix theory, IEEE Transactions on Signal Processing, vol.57, issue.10, pp.3930-3941, 2009.

R. Couillet, M. S. Greco, J. P. Ovarlez, and F. Pascal, RMT for whitening space correlation and applications to radar detection, 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, pp.149-152, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01262631

W. Hachem, P. Loubaton, X. Mestre, J. Najim, and P. Vallet, A subspace estimator for fixed rank perturbations of large random matrices, Journal of Multivariate Analysis, vol.114, pp.427-447, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00598826

R. Couillet, Robust spiked random matrices and a robust G-MUSIC estimator, Journal of Multivariate Analysis, vol.140, pp.139-161, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01242489

L. Laloux, P. Cizeau, J. Bouchaud, and M. Potters, Noise dressing of financial correlation matrices, Physycal Review Letters, vol.83, issue.1468, 1999.

L. Laloux, P. Cizeau, M. Potters, and J. Bouchaud, Random Matrix Theory and financial correlations, International Journal of Theoretical and Applied Finance, vol.3, issue.03, pp.391-397, 2000.

M. Potters, J. P. Bouchaud, and L. Laloux, Financial applications of Random Matrix Theory: old laces and new pieces, Acta Physica Polonica B, vol.36, issue.9, 2005.

V. Plerou, P. Gopikrishnan, B. Rosenow, L. A. Amaral, and H. E. Stanley, Collective behavior of stock price movements: A Random Matrix Theory approach, Physica A, vol.299, pp.175-180, 2001.

J. Vinogradova, R. Couillet, and W. Hachem, Statistical inference in large antenna arrays under unknown noise pattern, IEEE Transactions on Signal Processing, vol.61, issue.22, pp.5633-5645, 2013.
URL : https://hal.archives-ouvertes.fr/hal-02287071

E. Terreaux, J. P. Ovarlez, and F. Pascal, Robust model order selection in large dimensional Elliptically Symmetric noise, 2017.

, New model order selection in large dimension regime for Complex Elliptically Symmetric noise, 25th European Signal Processing Conference (EUSIPCO), pp.1090-1094, 2017.

, A Toeplitz-Tyler estimation of the model order in large dimensional regime, IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2018.

D. Kelker, Distribution theory of spherical distributions and a locationscale parameter generalization, Sankhy?: The Indian Journal of Statistics, Series A, vol.32, issue.4, pp.419-430, 1970.

E. Ollila, D. E. Tyler, V. Koivunen, and H. V. Poor, Complex Elliptically Symmetric distributions: Survey, new results and applications, IEEE Transactions on Signal Processing, vol.60, issue.11, pp.5597-5625, 2012.

J. M. Bioucas-dias, A. Plaza, N. Dobigeon, M. Parente, Q. Du et al., Hyperspectral unmixing overview: Geometrical, statistical, and sparse regression-based approaches, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol.5, issue.2, pp.354-379, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00760787

D. Melas, R. Suryanarayanan, and S. Cavaglia, Efficient replication of factor returns, 2009.

E. Jay, P. Duvaut, S. Darolles, and A. Chrétien, Multi-factor models: examining the potential of signal processing techniques, IEEE Signal Processing Magazine, vol.28, issue.5, 2011.

S. Darolles, P. Duvaut, and E. Jay, Multi-factor models and signal processing techniques: Application to quantitative finance, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01632892

S. Darolles, C. Gouriéroux, and E. Jay, Robust portfolio allocation with risk contribution restrictions, 2013.

F. Pascal, Y. Chitour, J. P. Ovarlez, P. Forster, and P. Larzabal, Covariance structure maximum-likelihood estimates in compound Gaussian noise: Existence and algorithm analysis, IEEE Transactions on Signal Processing, vol.56, issue.1, pp.34-48, 2008.
URL : https://hal.archives-ouvertes.fr/hal-01816367

F. Pascal, P. Forster, J. P. Ovarlez, and P. Larzabal, Performance analysis of covariance matrix estimates in impulsive noise, IEEE Transactions on Signal Processing, vol.56, issue.6, pp.2206-2217, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00353591

M. Mahot, F. Pascal, P. Forster, and J. P. Ovarlez, Asymptotic properties of robust complex covariance matrix estimates, IEEE Transactions on Signal Processing, vol.61, issue.13, pp.3348-3356, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01705126

R. Couillet and M. Debbah, Random matrix methods for wireless communications, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00658725

S. Kritchman and B. Nadler, Non-parametric detection of the number of signals: Hypothesis testing and random matrix theory, IEEE Transactions on Signal Processing, vol.57, issue.10, pp.3930-3941, 2009.

R. Couillet, M. S. Greco, J. P. Ovarlez, and F. Pascal, RMT for whitening space correlation and applications to radar detection, IEEE CAMSAP, pp.149-152, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01262631

W. Hachem, P. Loubaton, X. Mestre, J. Najim, and P. Vallet, A subspace estimator for fixed rank perturbations of large random matrices, Journal of Multivariate Analysis, vol.114, pp.427-447, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00598826

R. Couillet, Robust spiked random matrices and a robust G-MUSIC estimator, Journal of Mult. Analysis, vol.140, pp.139-161, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01242489

V. A. Marchenko and L. A. Pastur, Distribution of eigenvalues for some sets of random matrices, Matematicheskii Sbornik, 1967.

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