U. Amato, A. Antoniadis, and I. De-feis, Dimension reduction in functional regression with applications, Computational Statistics & Data Analysis, vol.50, issue.9, pp.2422-2446, 2006.
DOI : 10.1016/j.csda.2004.12.007

URL : https://hal.archives-ouvertes.fr/hal-00103266

Y. Aragon, A gauss implementation of multivariate sliced inverse regression, Computational Statistics, vol.12, pp.355-372, 1997.

Y. Aragon and J. Saracco, Sliced Inverse Regression (SIR): an appraisal of small sample alternatives to slicing, Computational Statistics, vol.12, pp.109-130, 1997.

R. Aza¨?saza¨?s, A. Gégout-petit, and J. Saracco, Optimal quantization applied to sliced inverse regression, Journal of Statistical Planning and Inference, vol.142, issue.2, pp.481-492, 2012.
DOI : 10.1016/j.jspi.2011.08.006

Z. D. Bai and X. He, A chi-square test for dimensionality with non-Gaussian data, Journal of Multivariate Analysis, vol.88, issue.1, pp.109-117, 2004.
DOI : 10.1016/S0047-259X(03)00056-3

L. Barreda, A. Gannoun, and J. Saracco, Some extensions of multivariate sliced inverse regression, Journal of Statistical Computation and Simulation, vol.15, issue.1, pp.1-17, 2007.
DOI : 10.1080/10629360600687840

M. P. Barrios and S. Velilla, A bootstrap method for assessing the dimension of a general regression problem, Statistics & Probability Letters, vol.77, issue.3, pp.247-255, 2007.
DOI : 10.1016/j.spl.2006.07.020

C. Bernard-michel, S. Douté, M. Fauvel, L. Gardes, and S. Girard, Retrieval of Mars surface physical properties from OMEGA hyperspectral images using regularized sliced inverse regression, Journal of Geophysical Research, vol.20, issue.2, 2009.
DOI : 10.1029/2008JE003171

URL : https://hal.archives-ouvertes.fr/inria-00276116

C. Bernard-michel, L. Gardes, and S. Girard, A Note on Sliced Inverse Regression with Regularizations, Biometrics, vol.21, issue.3, pp.982-986, 2008.
DOI : 10.1111/j.1541-0420.2008.01080.x

URL : https://hal.archives-ouvertes.fr/inria-00180496

C. Bernard-michel, L. Gardes, and S. Girard, Gaussian Regularized Sliced Inverse Regression, Statistics and Computing, vol.5, issue.22, pp.85-98, 2009.
DOI : 10.1007/s11222-008-9073-z

URL : https://hal.archives-ouvertes.fr/inria-00180458

E. Bura and R. D. Cook, Estimating the structural dimension of regressions via parametric inverse regression, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.63, issue.2, pp.393-410, 2001.
DOI : 10.1111/1467-9868.00292

M. Chavent, V. Kuentz, B. Liquet, and J. Saracco, A Sliced Inverse Regression Approach for a Stratified Population, Communications in statistics -Theory and methods 40, pp.1-22, 2011.
DOI : 10.1214/aos/1032526955

C. H. Chen and K. C. Li, Can SIR be as popular as multiple linear regression?, Statistica Sinica, vol.8, pp.289-316, 1998.

P. Cí?ek and W. Härdle, Robust estimation of dimension reduction space, Computational Statistics & Data Analysis, vol.51, issue.2, pp.545-555, 2006.
DOI : 10.1016/j.csda.2005.11.001

R. D. Cook, On the Interpretation of Regression Plots, Journal of the American Statistical Association, vol.41, issue.425, pp.177-189, 1994.
DOI : 10.1214/aos/1176347254

R. D. Cook, Principal Hessian Directions Revisited, Journal of the American Statistical Association, vol.18, issue.441, pp.84-100, 1998.
DOI : 10.1080/01621459.1998.10474090

R. D. Cook, Save: a method for dimension reduction and graphics in regression, Communications in Statistics - Theory and Methods, vol.41, issue.9-10, pp.2109-2121, 2000.
DOI : 10.2307/2290640

R. D. Cook, Regression Graphics: Ideas for Studying Regressions Through Graphics, 2009.

R. D. Cook and B. Li, Dimension reduction for conditional mean in regression, The Annals of Statistics, vol.30, issue.2, pp.450-474, 2002.
DOI : 10.1214/aos/1021379861

R. D. Cook and C. J. Nachtsheim, Reweighting to Achieve Elliptically Contoured Covariates in Regression, Journal of the American Statistical Association, vol.21, issue.426, pp.592-599, 1994.
DOI : 10.1002/0471725218

R. D. Cook and C. M. Setodji, A Model-Free Test for Reduced Rank in Multivariate Regression, Journal of the American Statistical Association, vol.98, issue.462, pp.340-351, 2003.
DOI : 10.1198/016214503000134

S. Douté, B. Schmitt, Y. Langevin, J. P. Bibring, F. Altieri et al., South Pole of Mars: Nature and composition of the icy terrains from Mars Express OMEGA observations, Planetary and Space Science, vol.55, issue.1-2, pp.113-133, 2007.
DOI : 10.1016/j.pss.2006.05.035

N. Duan and K. C. Li, Slicing Regression: A Link-Free Regression Method, The Annals of Statistics, vol.19, issue.2, pp.505-530, 1991.
DOI : 10.1214/aos/1176348109

A. Gannoun, S. Girard, C. Guinot, and J. Saracco, Sliced inverse regression in reference curves estimation, Computational Statistics & Data Analysis, vol.46, issue.1, pp.103-122, 2004.
DOI : 10.1016/S0167-9473(03)00141-5

URL : https://hal.archives-ouvertes.fr/hal-00724646

A. Gannoun and J. Saracco, An asymptotic theory for SIR? method, Statistica Sinica, vol.13, pp.297-310, 2003.

P. Hall and K. C. Li, On almost Linearity of Low Dimensional Projections from High Dimensional Data, The Annals of Statistics, vol.21, issue.2, pp.867-889, 1993.
DOI : 10.1214/aos/1176349155

H. Hino, K. Wakayama, and N. Murata, Entropy-based sliced inverse regression, Computational Statistics & Data Analysis, vol.67, pp.105-114, 2013.
DOI : 10.1016/j.csda.2013.05.017

T. Hsing, Nearest neighbor inverse regression, The Annals of Statistics, vol.27, issue.2, pp.697-731, 1999.
DOI : 10.1214/aos/1018031213

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.
DOI : 10.1214/aos/1176348669

V. Kuentz, B. Liquet, and J. Saracco, Bagging versions of sliced inverse regression. Communications in statistics -Theory and methods 39, 1985.
URL : https://hal.archives-ouvertes.fr/hal-00389125

V. Kuentz and J. Saracco, Cluster-based Sliced Inverse Regression, Journal of the Korean Statistical Society, vol.39, issue.2, pp.251-267, 2010.
DOI : 10.1016/j.jkss.2009.08.004

URL : https://hal.archives-ouvertes.fr/hal-00547252

B. Li, S. Wen, and L. Zhu, On a Projective Resampling Method for Dimension Reduction With Multivariate Responses, Journal of the American Statistical Association, vol.103, issue.483, pp.1177-1186, 2008.
DOI : 10.1198/016214508000000445

K. C. Li, Sliced Inverse Regression for Dimension Reduction, Journal of the American Statistical Association, vol.13, issue.414, pp.316-342, 1991.
DOI : 10.1214/aos/1176345514

K. C. Li, On Principal Hessian Directions for Data Visualization and Dimension Reduction: Another Application of Stein's Lemma, Journal of the American Statistical Association, vol.13, issue.420, pp.1025-1039, 1992.
DOI : 10.1002/9780470316818

K. C. Li, Y. Aragon, K. Shedden, and C. T. Agnan, Dimension Reduction for Multivariate Response Data, Journal of the American Statistical Association, vol.98, issue.461, pp.99-109, 2003.
DOI : 10.1198/016214503388619139

L. Li and C. J. Nachtsheim, Sparse Sliced Inverse Regression, Technometrics, vol.48, issue.4, pp.503-510, 2006.
DOI : 10.1198/004017006000000129

L. Li and X. Yin, Sliced Inverse Regression with Regularizations, Biometrics, vol.67, issue.1, pp.124-131, 2008.
DOI : 10.1111/j.1541-0420.2007.00836.x

B. Liquet and J. Saracco, A graphical tool for selecting the number of slices and the dimension of the model in SIR and SAVE approaches, Computational Statistics, vol.98, issue.1, pp.103-125, 2012.
DOI : 10.1007/s00180-011-0241-9

URL : https://hal.archives-ouvertes.fr/hal-00938090

H. H. Lue, Sliced inverse regression for multivariate response regression, Journal of Statistical Planning and Inference, vol.139, issue.8, pp.2656-2664, 2009.
DOI : 10.1016/j.jspi.2008.12.006

G. M. Nkiet, Consistent estimation of the dimensionality in sliced inverse regression, Annals of the Institute of Statistical Mathematics, vol.93, issue.2, pp.257-271, 2008.
DOI : 10.1007/s10463-006-0106-0

L. A. Prendergast, Influence Functions for Sliced Inverse Regression, Scandinavian Journal of Statistics, vol.5, issue.3, pp.385-404, 2005.
DOI : 10.1111/1467-9868.03411

L. A. Prendergast, Implications of influence function analysis for sliced inverse regression and sliced average variance estimation, Biometrika, vol.94, issue.3, pp.585-601, 2007.
DOI : 10.1093/biomet/asm055

J. Saracco, An asymptotic theory for Sliced Inverse Regression Communications in statistics -Theory and methods 26, pp.2141-2171, 1997.

J. Saracco, Sliced inverse regression under linear constraints Communications in statistics -Theory and methods 28, pp.2367-2393, 1999.

J. Saracco, POOLED SLICING METHODS VERSUS SLICING METHODS, Communications in statistics -Simulation and Computation, pp.489-511, 2001.
DOI : 10.1093/biomet/58.1.105

J. Saracco, Asymptotics for pooled marginal slicing estimator based on <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msub><mml:mrow><mml:mi>SIR</mml:mi></mml:mrow><mml:mrow><mml:mi>??</mml:mi></mml:mrow></mml:msub></mml:math> approach, Journal of Multivariate Analysis, vol.96, issue.1, pp.117-135, 2005.
DOI : 10.1016/j.jmva.2004.10.003

J. R. Schott, Determining the Dimensionality in Sliced Inverse Regression, Journal of the American Statistical Association, vol.16, issue.425, pp.141-148, 1994.
DOI : 10.1214/aos/1176345514

L. Scrucca, Class prediction and gene selection for DNA microarrays using regularized sliced inverse regression, Computational Statistics & Data Analysis, vol.52, issue.1, pp.438-451, 2007.
DOI : 10.1016/j.csda.2007.02.005

L. Scrucca, Model-based SIR for dimension reduction, Computational Statistics & Data Analysis, vol.55, issue.11, pp.3010-3026, 2011.
DOI : 10.1016/j.csda.2011.05.006

C. M. Setodji and R. D. Cook, -Means Inverse Regression, Technometrics, vol.46, issue.4, pp.421-429, 2004.
DOI : 10.1198/004017004000000437

Y. Shao, R. D. Cook, and S. Weisberg, Partial central subspace and sliced average variance estimation, Journal of Statistical Planning and Inference, vol.139, issue.3, pp.952-961, 2009.
DOI : 10.1016/j.jspi.2008.06.002

M. E. Szretter and V. J. Yohai, The sliced inverse regression algorithm as a maximum likelihood procedure, Journal of Statistical Planning and Inference, vol.139, issue.10, pp.3570-3578, 2009.
DOI : 10.1016/j.jspi.2009.04.008

D. E. Tyler, Asymptotic Inference for Eigenvectors, The Annals of Statistics, vol.9, issue.4, pp.725-736, 1981.
DOI : 10.1214/aos/1176345514

H. M. Wu, Kernel Sliced Inverse Regression with Applications to Classification, Journal of Computational and Graphical Statistics, vol.17, issue.3, pp.590-610, 2008.
DOI : 10.1198/106186008X345161

Y. Xia, H. Tong, W. K. Li, and L. X. Zhu, An adaptive estimation of dimension reduction space, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.24, issue.3, pp.363-410, 2002.
DOI : 10.1111/1467-9868.03411

X. Yin and E. Bura, Moment-based dimension reduction for multivariate response regression, Journal of Statistical Planning and Inference, vol.136, issue.10, pp.3675-3688, 2006.
DOI : 10.1016/j.jspi.2005.01.011

J. K. Yoo, Iterative optimal sufficient dimension reduction for conditional mean in multivariate regression, Journal of Data Science, vol.7, pp.267-276, 2009.

L. Zhu, B. Miao, and H. Peng, On Sliced Inverse Regression With High-Dimensional Covariates, Journal of the American Statistical Association, vol.101, issue.474, pp.630-643, 2006.
DOI : 10.1198/016214505000001285

L. P. Zhu and Z. Yu, On spline approximation of sliced inverse regression, Science in China Series A: Mathematics, vol.36, issue.9, pp.1289-1302, 2007.
DOI : 10.1007/s11425-007-0085-5

L. P. Zhu, L. X. Zhu, and Z. H. Feng, Dimension Reduction in Regressions Through Cumulative Slicing Estimation, Journal of the American Statistical Association, vol.105, issue.492, pp.1455-1466, 2010.
DOI : 10.1198/jasa.2010.tm09666

L. P. Zhu, L. X. Zhu, and S. Q. Wen, On dimension reduction in regressions with multivariate responses, Statistica Sinica, vol.20, pp.1291-1307, 2010.

L. X. Zhu and K. T. Fang, Asymptotics for kernel estimate of sliced inverse regression, The Annals of Statistics, vol.24, issue.3, pp.1053-1068, 1996.
DOI : 10.1214/aos/1032526955

L. X. Zhu and K. W. Ng, Asymptotics of sliced inverse regression, Statistica Sinica, vol.5, pp.727-736, 1995.

L. X. Zhu, M. Ohtaki, and Y. Li, On hybrid methods of inverse regression-based algorithms, Computational Statistics & Data Analysis, vol.51, issue.5, pp.2621-2635, 2007.
DOI : 10.1016/j.csda.2006.01.005