A. Hyvärinen, Estimation of non-normalized statistical models by score matching, Journal of Machine Learning Research, vol.6, p.695709, 2005.

G. Arfken and D. , Mathematical Methods for Physicists, pp.37-42, 1985.
DOI : 10.1063/1.3034326

A. Argyriou, T. Evgeniou, and M. Pontil, Convex multi-task feature learning, Machine Learning, vol.73, pp.243-272, 2008.
DOI : 10.1007/s10994-007-5040-8
URL : https://link.springer.com/content/pdf/10.1007%2Fs10994-007-5040-8.pdf

S. Boucheron, G. Lugosi, and P. Massart, Concentration inequalities: A nonasymptotic theory of independence, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00794821

D. R. Brillinger, A Generalized Linear Model with 'Gaussian' Regressor Variables, Woodsworth International Group, 1982.
DOI : 10.1007/978-1-4614-1344-8_34

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.

R. D. Cook, Save: a method for dimension reduction and graphics in regression, Communications in Statistics-Theory and Methods, vol.29, pp.2109-2121, 2000.

R. D. Cook and H. Lee, Dimension Reduction in Binary Response Regression, Journal of the American Statistical Association, vol.94, pp.1187-1200, 1999.

R. D. Cook and S. Weisberg, Discussion of 'Sliced Inverse Regression, Journal of the American Statistical Association, vol.86, pp.328-332, 1991.

A. S. Dalalyan, A. Juditsky, and V. Spokoiny, A new algorithm for estimating the effective dimension-reduction subspace, Journal of Machine Learning Research, vol.9, pp.1647-1678, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00128129

N. Duan and K. Li, Slicing regression: a link-free regression method, The Annals of Statistics, vol.19, pp.505-530, 1991.

K. Fukumizu, F. R. Bach, and M. I. Jordan, Kernel dimension reduction in regression, The Annals of Statistics, vol.37, pp.1871-1905, 2009.

L. Gyrfi, M. Kohler, A. Krzyzak, and H. Walk, A distribution-free theory of nonparametric regression, Springer series in statistics, 2002.

J. Hooper, Simultaneous Equations and Canonical Correlation Theory, Econometrica, vol.27, pp.245-256, 1959.

M. Hristache, A. Juditsky, and V. Spokoiny, Direct estimation of the index coefficient in a single index model, The Annals of Statistics, vol.29, issue.3, pp.595-623, 2001.

T. Hsing and R. J. Carroll, An asymptotic theory for sliced inverse regression, The Annals of Statistics, vol.20, issue.2, pp.1040-1061, 1992.

A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis, vol.46, 2004.

M. Janzamin, H. Sedghi, and A. Anandkumar, Score function features for discriminative learning: Matrix and tensor framework, CoRR, 2014.

, Generalization Bounds for Neural Networks through Tensor Factorization, CoRR, 2015.

K. Li, Sliced Inverse Regression for Dimensional Reduction, Journal of the American Statistical Association, vol.86, pp.316-327, 1991.

, On Principal Hessian Directions for Data Visualization and Dimension Reduction: Another Application of Stein's Lemma, Journal of the American Statistical Association, vol.87, pp.1025-1039, 1992.

K. Li and N. Duan, Regression analysis under link violation, The Annals of Statistics, vol.17, p.10091052, 1989.

Q. Lin, Z. Zhao, and J. S. Liu, On consistency and sparsity for sliced inverse regression in high dimensions, The Annals of Statistics, vol.46, pp.580-610, 2018.

M. Mcdonald, A. M. , and S. Stamos, Spectral k-support norm regularization, Advances in Neural Information Processing Systems, 2014.

C. Stein, Estimation of the Mean of a Multivariate Normal Distribution, The Annals of Statistics, vol.9, pp.1135-1151, 1981.

G. Stewart and J. Sun, Matrix perturbation theory (computer science and scientific computing), 1990.

T. Stoker, Consistent estimation of scaled coefficients, Econometrica, vol.54, p.14611481, 1986.

A. B. Tsybakov, Introduction to Nonparametric Estimation, 2009.

V. Q. Vu and J. Lei, Minimax sparse principal subspace estimation in high dimensions, The Annals of Statistics, pp.2905-2947, 2013.

H. Wang and Y. Xia, On directional regression for dimension reduction, J. Amer. Statist. Ass, 2007.

, Sliced regression for dimension reduction, Journal of the American Statistical Association, vol.103, pp.811-821, 2008.

J. W. Donoghue, Monotone Matrix Functions and Analytic Continuation, 1974.

Y. Xia, H. Tong, W. Li, and L. Zhu, An adaptive estimation of dimension reduction space, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.64, pp.363-410, 2002.

Y. Xia, H. Tong, W. K. Li, and L. Zhu, An adaptive estimation of dimension reduction space, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.64, pp.363-410, 2002.

S. S. Yang, General distribution theory of the concomitants of order statistics, vol.5, pp.996-1002, 1977.

Y. Yu, T. Wang, and R. J. Samworth, A useful variant of the davis-kahan theorem for statisticians, Biometrika, vol.102, pp.315-323, 2015.