P. Absil, R. Mahony, and R. Sepulchre, Optimization Algorithms on Matrix Manifolds, 2008.
DOI : 10.1515/9781400830244

S. M. Ali and S. D. Silvey, A general class of coefficients of divergence of one distribution from another, Journal of the Royal Statistical Society, Series B, vol.28, issue.1, pp.131-142, 1966.

S. Amari and A. Cichocki, Information geometry of divergence functions, Bulletin of the Polish Academy of Sciences: Technical Sciences, vol.58, issue.1, pp.183-195, 2010.
DOI : 10.2478/v10175-010-0019-1

L. Ambrosio, N. Gigli, and G. Savare, Gradient flows in metric spaces and in the space of probability measures, Lectures in Mathematics ETH Zurich. Birkhauser, 2005.

R. D. Anderson and V. L. Klee-jr, Convex functions and upper semi-continuous collections, Duke Mathematical Journal, vol.19, issue.2, pp.349-357, 1952.
DOI : 10.1215/S0012-7094-52-01935-2
URL : http://projecteuclid.org/download/pdf_1/euclid.dmj/1077477218

M. Arnaudon, F. Barbaresco, and L. Yang, Riemannian Medians and Means With Applications to Radar Signal Processing, IEEE Journal of Selected Topics in Signal Processing, vol.7, issue.4, pp.595-604, 2013.
DOI : 10.1109/JSTSP.2013.2261798

M. Arnaudon and L. Miclo, A stochastic algorithm finding $p$-means on the circle, Bernoulli, vol.22, issue.4, 2013.
DOI : 10.3150/15-BEJ728
URL : https://hal.archives-ouvertes.fr/hal-00781715

F. Aurenhammer, Power Diagrams: Properties, Algorithms and Applications, SIAM Journal on Computing, vol.16, issue.1, pp.78-96, 1987.
DOI : 10.1137/0216006

F. Aurenhammer, F. Hoffmann, and B. Aronov, Minkowski-Type Theorems and Least-Squares Clustering, Algorithmica, vol.20, issue.1, pp.61-76, 1998.
DOI : 10.1007/PL00009187

F. Barbaresco, Super resolution spectrum analysis regularization : Burg, capon and ago antagonistic algorithms, Proc. EUSIPCO'96, pp.2005-2008, 1996.

F. Barbaresco, New foundation of radar doppler signal processing based on advanced differential geometry of symmetric spaces : Doppler matrix cfar and radar application, Radar09 Conference, 2009.

F. Barbaresco, Information Geometry of Covariance Matrix: Cartan-Siegel Homogeneous Bounded Domains, Mostow/Berger Fibration and Fr??chet Median, Matrix Information Geometry, 2012.
DOI : 10.1007/978-3-642-30232-9_9

F. Barbaresco, Koszul Information Geometry and Souriau Geometric Temperature/Capacity of Lie Group Thermodynamics, Entropy, vol.16, issue.8, pp.4521-4565, 2014.
DOI : 10.3390/e16084521

T. J. Barnard and D. D. Weiner, Non-Gaussian clutter modeling with generalized spherically invariant random vectors, IEEE Transactions on Signal Processing, vol.44, issue.10, pp.2384-2390, 1996.
DOI : 10.1109/78.539023

B. A. Basu, I. R. Harris, N. L. Hjort, and M. C. Jones, Robust and efficient estimation by minimising a density power divergence, Biometrika, vol.85, issue.3, pp.549-559, 1998.
DOI : 10.1093/biomet/85.3.549

S. Bausson, F. Pascal, P. Forster, J. P. Ovarlez, and P. Larzabal, First- and Second-Order Moments of the Normalized Sample Covariance Matrix of Spherically Invariant Random Vectors, IEEE Signal Processing Letters, vol.14, issue.6, pp.425-428, 2007.
DOI : 10.1109/LSP.2006.888400
URL : https://hal.archives-ouvertes.fr/halshs-00158262

J. Bensadon, Black-Box Optimization Using Geodesics in Statistical Manifolds, Entropy, vol.17, issue.1, 2013.
DOI : 10.3390/e17010304

M. Berkane, K. Oden, and P. M. Bentler, Geodesic Estimation in Elliptical Distributions, Journal of Multivariate Analysis, vol.63, issue.1, pp.35-46, 1997.
DOI : 10.1006/jmva.1997.1690

P. Bertail, Empirical likelihood in some semiparametric models, Bernoulli, vol.12, issue.2, pp.299-331, 2006.
DOI : 10.3150/bj/1145993976

O. Besson and Y. Abramovich, On the Fisher Information Matrix for Multivariate Elliptically Contoured Distributions, IEEE Signal Processing Letters, vol.20, issue.11, pp.1130-1133, 2013.
DOI : 10.1109/LSP.2013.2281914
URL : https://hal.archives-ouvertes.fr/hal-00867012

R. Bhatia, Positive Definite Matrices, 2007.
DOI : 10.1515/9781400827787
URL : https://hal.archives-ouvertes.fr/hal-01500514

D. A. Bini, B. Iannazzo, B. Jeuris, and R. Vandebril, Geometric means of structured matrices, BIT Numerical Mathematics, vol.14, issue.3, pp.55-83, 2014.
DOI : 10.1007/s10543-013-0450-4

X. Blanc, C. L. Bris, and P. Lions, From molecular models to continuum mechanics . Archive for Rational Mechanics and Analysis, pp.341-381, 2002.
DOI : 10.1007/s00205-002-0218-5
URL : https://hal.archives-ouvertes.fr/hal-01487687

X. Blanc, C. L. Bris, and P. Lions, Atomistic to Continuum limits for computational materials science, ESAIM: Mathematical Modelling and Numerical Analysis, vol.41, issue.2, pp.391-426, 2007.
DOI : 10.1051/m2an:2007018
URL : https://hal.archives-ouvertes.fr/hal-00667335

J. M. Borwein and A. S. Lewis, Duality Relationships for Entropy-Like Minimization Problems, SIAM Journal on Control and Optimization, vol.29, issue.2, pp.325-338, 1991.
DOI : 10.1137/0329017

G. E. Box and D. R. Cox, An analysis of transformations, Journal of the Royal Statistical Society. Series B (Methodological), vol.26, issue.2, pp.211-252, 1964.

Y. Brenier, Polar factorization and monotone rearrangement of vector-valued functions, Communications on Pure and Applied Mathematics, vol.117, issue.4, pp.375-417, 1991.
DOI : 10.1002/cpa.3160440402

P. J. Brockwell and R. Dalhaus, Generalized Levinson???Durbin and Burg algorithms, Journal of Econometrics, vol.118, issue.1-2, pp.129-149, 2003.
DOI : 10.1016/S0304-4076(03)00138-6

M. Broniatowski and A. Keziou, Divergences and duality for estimation and test under moment condition models, Journal of Statistical Planning and Inference, vol.142, issue.9, pp.2554-2573, 2012.
DOI : 10.1016/j.jspi.2012.03.013

M. Broniatowski and I. Vajda, Several applications of divergence criteria in continuous families, Kybernetika, vol.48, issue.4, pp.600-636, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00430179

J. P. Burg, Maximum entropy spectral analysis. Modern Spectrum Analysis, pp.34-41, 1978.

S. Cambanis, S. Huang, and G. Simons, On the theory of elliptically contoured distributions, Journal of Multivariate Analysis, vol.11, issue.3, pp.368-385, 1981.
DOI : 10.1016/0047-259X(81)90082-8

J. Capon, High resolution frequency-wavenumber spectral analysis, Proceedings of the IEEE, pp.1408-1418, 1969.
DOI : 10.1109/proc.1969.7278

G. Carlier, A. Galichon, and F. Santambrogio, From Knothe's Transport to Brenier's Map and a Continuation Method for Optimal Transport, SIAM Journal on Mathematical Analysis, vol.41, issue.6, pp.412554-2576, 2009.
DOI : 10.1137/080740647

J. Carretero-moya, J. Gismero-menoyo, A. Asensio-lopez, and A. Blanco-del-campo, Small-Target Detection in High-Resolution Heterogeneous Sea-Clutter: An Empirical Analysis, IEEE Transactions on Aerospace and Electronic Systems, vol.47, issue.3, pp.471880-1898, 2011.
DOI : 10.1109/TAES.2011.5937271

E. Cartan, Groupes simples clos et ouverts et géométrie riemannienne, J. Math. pures et appl, vol.8, pp.1-33, 1929.

L. K. Chan, On a Characterization of Distributions by Expected Values of Extreme Order Statistics, The American Mathematical Monthly, vol.74, issue.8, pp.950-951, 1967.
DOI : 10.2307/2315271

J. T. Chang and D. Pollard, Conditioning as disintegration, Statistica Neerlandica, vol.51, issue.3, pp.287-317, 1997.
DOI : 10.1111/1467-9574.00056
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.408.4523

P. Chaudhuri, On a Geometric Notion of Quantiles for Multivariate Data, Journal of the American Statistical Association, vol.24, issue.434, pp.91862-872, 1996.
DOI : 10.1080/01621459.1996.10476954

E. Conte, A. De-maio, and G. Galdi, Recursive estimation of the covariance matrix of a compound-gaussian process and its application to adaptative cfar detection, IEEE Transactions on Signal Processing, issue.8, pp.501908-1915, 2002.

E. Conte and M. Longo, Characterization of radar clutter as a spherically invariant random process, IEE Proc.-Pt.F, pp.191-197, 1987.

I. Csiszár, Eine informationstheoretische ungleichung und ihre anwendung auf den beweis der ergodizitat von markoffschen ketten, Magyar. Tud. Akad. Mat. Kutato Int. Kozl, vol.8, pp.85-108, 1963.

I. Csiszár, F. Gamboa, and E. Gassiat, Mem pixel correlated solutions for generalized moment and interpolation problems, IEEE Trans. Inform. Theory, issue.7, pp.452253-2270, 1999.

I. Csiszár and F. Matú?, Generalized minimizers of convex functionals, bregman distance, pythagorean identities, Kybernetika, vol.48, issue.4, pp.637-689, 2012.

H. A. David, Order Statistics, 1981.
DOI : 10.1002/0471722162

M. P. Carmo, Riemannian geometry, 1992.
DOI : 10.1007/978-1-4757-2201-7

G. S. Easton and R. E. Mcculloch, A Multivariate Generalization of Quantile-Quantile Plots, Journal of the American Statistical Association, vol.55, issue.410, pp.376-386, 1990.
DOI : 10.1007/BF00423145

S. Eguchi and Y. Kano, Robusting maximum likelihood estimation by psidivergence, Tokyo : Institute of Statistical Mathematics, 2001.

J. H. Einmahl and D. M. Mason, Generalized Quantile Processes, The Annals of Statistics, vol.20, issue.2, pp.1062-1078, 1992.
DOI : 10.1214/aos/1176348670
URL : http://repository.tue.nl/683226

E. Elamir and A. Seheult, Trimmed L-moments, Computational Statistics & Data Analysis, vol.43, issue.3, pp.299-314, 2003.
DOI : 10.1016/S0167-9473(02)00250-5

M. Fréchet, Les éléments aléatoires de natures quelconque dans un espace distancié, Annales de l'IHP, pp.215-310, 1948.

H. Fujisawa, Normalized estimating equation for robust parameter estimation, Electronic Journal of Statistics, vol.7, issue.0, pp.1587-1606, 2013.
DOI : 10.1214/13-EJS817
URL : http://projecteuclid.org/download/pdfview_1/euclid.ejs/1369919743

H. Fujisawa and S. Eguchi, Robust parameter estimation with a small bias against heavy contamination, Journal of Multivariate Analysis, vol.99, issue.9, pp.2053-2081, 2008.
DOI : 10.1016/j.jmva.2008.02.004
URL : http://doi.org/10.1016/j.jmva.2008.02.004

A. Galichon and M. Henry, Dual theory of choice with multivariate risks, Journal of Economic Theory, vol.147, issue.4, pp.1501-1516, 2012.
DOI : 10.1016/j.jet.2011.06.002

F. Gini, Sub-optimum coherent radar detection in a mixture of K-distributed and Gaussian clutter, IEE Proceedings - Radar, Sonar and Navigation, vol.144, issue.1, pp.39-48, 1997.
DOI : 10.1049/ip-rsn:19970967

V. P. Godambe and M. E. Thompson, An extension of quasi-likelihood estimation, Journal of Statistical Planning and Inference, vol.22, issue.2, pp.137-172, 1989.
DOI : 10.1016/0378-3758(89)90106-7

C. Gourieroux and J. Jasiak, Dynamic quantile models, Journal of Econometrics, vol.147, issue.1, pp.198-205, 2008.
DOI : 10.1016/j.jeconom.2008.09.028

X. Gu, F. Luo, J. Sun, and S. Yau, Variational principles for Minkowski type problems, discrete optimal transport, and discrete Monge???Amp??re equations, Asian Journal of Mathematics, vol.20, issue.2, 2013.
DOI : 10.4310/AJM.2016.v20.n2.a7

M. Hallin, H. Oja, and D. Paindaveine, Semiparametrically efficient rank-based inference for shape. II. Optimal R -estimation of shape, The Annals of Statistics, vol.34, issue.6, pp.2757-2789, 2006.
DOI : 10.1214/009053606000000948

F. R. Hampel, E. M. Ronchetti, P. J. Rousseuw, and W. Stahel, Robust Statistics : The approach Based on Influence Functions, 1986.
DOI : 10.1002/9781118186435

L. P. Hansen, Large Sample Properties of Generalized Method of Moments Estimators, Econometrica, vol.50, issue.4, pp.1029-1054, 1982.
DOI : 10.2307/1912775

L. P. Hansen, Finite-sample properties of some alternative gmm estimators, Journal of Business and Economic Statistics, vol.14, issue.3, pp.262-280, 1996.
DOI : 10.1080/07350015.1996.10524656
URL : http://dspace.mit.edu/bitstream/1721.1/47970/1/finitesampleprop00hans.pdf

J. R. Hosking, Some theoretical results concerning l-moments, 1989.

J. R. Hosking, L-moments : analysis and estimation of distributions using linear combinations of order statistics, Journal of the Royal Statistical Society, vol.52, issue.1, pp.105-124, 1990.

J. R. Hosking and J. R. Wallis, Regional Frequency Analysis : An approach based on L-moments, 1997.
DOI : 10.1017/CBO9780511529443

P. J. Huber and E. M. Ronchetti, Robust Statistics. Second Edition, 2009.
DOI : 10.1002/0471725250

E. Jakeman, On the statistics of K-distributed noise, Journal of Physics A: Mathematical and General, vol.13, issue.1, pp.31-48, 1980.
DOI : 10.1088/0305-4470/13/1/006

E. Jurczenko, B. Maillet, and P. Merlin, Hedge fund portfolio selection with higherorder moments : a nonparametric mean-variance-skewness-kurtosis efficient frontier. Multi-moment asset allocation and pricing models, pp.21-66, 2006.

H. Karcher, Riemannian center of mass and mollifier smoothing, Communications on Pure and Applied Mathematics, vol.3, issue.5, pp.509-541, 1977.
DOI : 10.1002/cpa.3160300502

H. Karcher, Riemannian center of mass and so called karcher mean, 2014.

A. G. Konheim, A Note on Order Statistics, The American Mathematical Monthly, vol.78, issue.5, p.524, 1971.
DOI : 10.2307/2317761

S. Kraut, L. L. Scharf, and L. T. Mcwhorter, Adaptive subspace detectors, IEEE Transactions on Signal Processing, vol.49, issue.1, pp.1-16, 2001.
DOI : 10.1109/78.890324
URL : http://hdl.handle.net/10217/752

K. Kreutz-delgado, The complex gradient operator and the CR calculus, 2009.

C. and L. Bris, Systèmes multi-échelles : modélisation et simulation, SMAI, Mathématiques et Applications, p.47, 2005.
DOI : 10.1007/3-540-37671-2

E. L. Lehmann, Some Concepts of Dependence, The Annals of Mathematical Statistics, vol.37, issue.5, pp.1137-1153, 1966.
DOI : 10.1214/aoms/1177699260

F. Liese, Estimates of hellinger integrals of infinitely divisible distributions, Kybernetika, vol.23, issue.3, pp.227-238, 1987.

M. Mahot, Estimation robuste de la matrice de covariance en traitement du signal, Thèse de doctorat, 2012.
URL : https://hal.archives-ouvertes.fr/tel-00906143

R. A. Maronna, Robust $M$-Estimators of Multivariate Location and Scatter, The Annals of Statistics, vol.4, issue.1, pp.51-67, 1976.
DOI : 10.1214/aos/1176343347

R. J. Mccann, Existence and uniqueness of monotone measure-preserving maps, Duke Mathematical Journal, vol.80, issue.2, pp.309-323, 1995.
DOI : 10.1215/S0012-7094-95-08013-2

G. Meyer, S. Bonnabel, and R. Sepulchre, Regression on fixed-rank positive semidefinite matrices : A riemannian approach, Journal of Machine Learning Research, vol.12, pp.593-625, 2011.

R. B. Nelsen, An Introduction to Copulas, 2006.
DOI : 10.1007/978-1-4757-3076-0

W. Newey and R. Smith, Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators, Econometrica, vol.72, issue.1, pp.219-255, 2004.
DOI : 10.1111/j.1468-0262.2004.00482.x
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.559.8138

E. Ollila, D. Tyler, V. Koivunen, and V. Poor, Complex Elliptically Symmetric Distributions: Survey, New Results and Applications, IEEE Transactions on Signal Processing, vol.60, issue.11, pp.605597-5625, 2012.
DOI : 10.1109/TSP.2012.2212433

Y. Ollivier, L. Arnold, A. Auger, and N. Hansen, Information-geometric optimization algorithms : a unifying picture via invariance principles, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00601503

A. Owen, Empirical Likelihood Ratio Confidence Regions, The Annals of Statistics, vol.18, issue.1, pp.90-120, 1990.
DOI : 10.1214/aos/1176347494
URL : http://projecteuclid.org/download/pdf_1/euclid.aos/1176347494

G. Pailloux, Estimation structurée de la covariance du bruit en détection adaptative, Thèse de doctorat, 2010.

E. Parzen, Nonparametric Statistical Data Modeling, Journal of the American Statistical Association, vol.55, issue.365, pp.105-121, 1979.
DOI : 10.1080/01621459.1979.10481621

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.
DOI : 10.1109/TSP.2007.914311
URL : https://hal.archives-ouvertes.fr/hal-00353591

M. Pavon and A. Ferrante, On the Geometry of Maximum Entropy Problems, SIAM Review, vol.55, issue.3, pp.415-439, 2013.
DOI : 10.1137/120862843

X. Pennec, P. Fillard, and N. Ayache, A Riemannian Framework for Tensor Computing, International Journal of Computer Vision, vol.6, issue.2, pp.41-66, 2006.
DOI : 10.1007/s11263-005-3222-z
URL : https://hal.archives-ouvertes.fr/inria-00070743

R. T. Rockafellar, Convex Analysis, 1970.
DOI : 10.1515/9781400873173

H. Rohling, Radar CFAR Thresholding in Clutter and Multiple Target Situations, IEEE Transactions on Aerospace and Electronic Systems, vol.19, issue.4, pp.608-621, 1983.
DOI : 10.1109/TAES.1983.309350

M. Rosenblatt, Remarks on a Multivariate Transformation, The Annals of Mathematical Statistics, vol.23, issue.3, pp.470-472, 1952.
DOI : 10.1214/aoms/1177729394

W. Rudin, Functional Analysis. Second Edition, 1991.

I. J. Schoenberg, Metric Spaces and Completely Monotone Functions, The Annals of Mathematics, vol.39, issue.4, pp.811-841, 1938.
DOI : 10.2307/1968466

T. Sei, Gradient modeling for multivariate quantitative data, Annals of the Institute of Statistical Mathematics, vol.32, issue.2, pp.675-688, 2011.
DOI : 10.1007/s10463-009-0261-1

R. Serfling, Quantile functions for multivariate analysis: approaches and applications, Statistica Neerlandica, vol.28, issue.2, pp.214-232, 2002.
DOI : 10.1006/jmva.1999.1894

R. Serfling, Equivariance and invariance properties of multivariate quantile and related functions, and the role of standardisation, Journal of Nonparametric Statistics, vol.72, issue.7, pp.915-936, 2010.
DOI : 10.1214/aos/1016218226

R. Serfling and P. Xiao, A contribution to multivariate L-moments: L-comoment matrices, Journal of Multivariate Analysis, vol.98, issue.9, pp.1765-1781, 2007.
DOI : 10.1016/j.jmva.2007.01.008

S. M. Stigler, Linear Functions of Order Statistics with Smooth Weight Functions, The Annals of Statistics, vol.2, issue.4, pp.676-693, 1974.
DOI : 10.1214/aos/1176342756

P. Stoica and R. L. Moses, Spectral Analysis of Signals, 2005.

W. Trench, An Algorithm for the Inversion of Finite Toeplitz Matrices, Journal of the Society for Industrial and Applied Mathematics, vol.12, issue.3, pp.515-522, 1964.
DOI : 10.1137/0112045

J. W. Tukey, WHICH PART OF THE SAMPLE CONTAINS THE INFORMATION?, Proceedings of the National Academy of Sciences, vol.53, issue.1, pp.127-134, 1965.
DOI : 10.1073/pnas.53.1.127

D. Tyler, A Distribution-Free $M$-Estimator of Multivariate Scatter, The Annals of Statistics, vol.15, issue.1, pp.234-251, 1987.
DOI : 10.1214/aos/1176350263

D. Tyler, Statistical analysis for the angular central Gaussian distribution on the sphere, Biometrika, vol.74, issue.3, pp.579-589, 1987.
DOI : 10.1093/biomet/74.3.579

A. W. Van and . Vaart, Asymptotic Statistics, 1998.

S. Verblunsky, On Positive Harmonic Functions: A Contribution to the Algebra of Fourier Series, Proc. London Math. Soc, pp.125-157, 1935.
DOI : 10.1112/plms/s2-38.1.125

C. Villani, Topics in Optimal Transportation, Graduate Studies in Mathematics. Amer. Math. Soc, vol.58, 2003.
DOI : 10.1090/gsm/058

C. Villani, Optimal transport, old and new, Grundlehren der Mathematischen Wissenschaften, vol.338, 2009.

K. D. Ward, R. J. Tough, and S. Watts, Sea clutter: Scattering, the K distribution and radar performance, Waves in Random and Complex Media, vol.17, issue.2, 2006.
DOI : 10.1049/el:19810394

L. Yang, Médianes de mesures de probabilité dans les variétés riemanniennes et applications à la détection de cibles radar, Thèse de doctorat, 2012.

S. S. Yang, General Distribution Theory of the Concomitants of Order Statistics, The Annals of Statistics, vol.5, issue.5, pp.996-1002, 1977.
DOI : 10.1214/aos/1176343954

Y. Zuo and R. Serfling, General notions of statistical depth function, The Annals of Statistics, vol.28, issue.2, pp.461-482, 2000.
DOI : 10.1214/aos/1016218226