A. References and . Agresti, Categorical Data Analysis, 2013.

J. P. Benzécri, L'analyse des données, Tome II: L'analyse des correspondances. Dunod, 1973.

A. Bhattacharya and D. B. Dunson, Simplex Factor Models for Multivariate Unordered Categorical Data, Journal of the American Statistical Association, vol.52, issue.2003, pp.362-377, 2012.
DOI : 10.1198/106186006X160050
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3728016

P. Bühlmann and S. Van-de-geer, Statistics for High-Dimensional Data, 2011.
DOI : 10.1007/978-3-642-20192-9

W. Buntine, Variational Extensions to EM and Multinomial PCA, Machine Learning: ECML 2002, pp.23-34, 2002.
DOI : 10.1007/3-540-36755-1_3
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.18.5167

E. J. Candes, C. A. Sing-long, and J. D. Trzasko, Unbiased Risk Estimates for Singular Value Thresholding and Spectral Estimators, IEEE Transactions on Signal Processing, vol.61, issue.19, pp.614643-4657, 2013.
DOI : 10.1109/TSP.2013.2270464

R. Christensen, Log-Linear Models, 2010.
DOI : 10.1007/978-1-4757-4111-7

M. Collins, S. Dasgupta, and R. E. Schapire, A generalization of principal component analysis to the exponential family, Advances in Neural Information Processing Systems, 2001.

J. and D. Leeuw, Gifi goes logistic

J. and D. Leeuw, History of non linear principal component analysis, Visualization and Verbalization of Data, 2014.

J. , D. Leeuw, and W. J. Heiser, Convergence of correction matrix algorithms for multidimensional scaling, Geometric Representations of Relational Data, pp.735-752, 1977.

J. De and L. , Principal component analysis of binary data by iterated singular value decomposition, Computational Statistics and Data Analysis, vol.50, issue.1, pp.21-39, 2006.

L. Donoho and I. M. Johnstone, Ideal spatial adaptation by wavelet shrinkage, Biometrika, vol.81, issue.3, pp.425-455, 1994.
DOI : 10.1093/biomet/81.3.425
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.124.5288

D. B. Dunson and C. Xing, Nonparametric Bayes Modeling of Multivariate Categorical Data, Journal of the American Statistical Association, vol.104, issue.487, pp.1042-1051, 2009.
DOI : 10.1198/jasa.2009.tm08439

M. Fazel, Matrix Rank Minimization with Applications, 2002.

M. Gavish and D. L. Donoho, Optimal Shrinkage of Singular Values, IEEE Transactions on Information Theory, vol.63, issue.4, 2014.
DOI : 10.1109/TIT.2017.2653801

C. Giacobino, S. Sardy, and N. Hengartner, Quantile universal threshold selection with an application in generalized model with lasso, 2016.

L. A. Goodman, Exploratory latent structure analysis using both identifiable and unidentifiable models, Biometrika, vol.61, issue.2, pp.255-231, 1974.
DOI : 10.1093/biomet/61.2.215

M. J. Greenacre, Theory and Applications of Correspondence Analysis, 1984.

M. J. Greenacre and J. Blasius, Multiple Correspondence Analysis and Related Methods, 2006.
DOI : 10.1201/9781420011319

J. Josse and S. Sardy, Adaptive shrinkage of singular values, Statistics and Computing, vol.101, issue.4, pp.1-10, 2015.
DOI : 10.1198/016214506000000735
URL : https://hal.archives-ouvertes.fr/hal-00905708

H. A. Kiers, Weighted least squares fitting using ordinary least squares algorithms, Psychometrika, vol.18, issue.2, pp.251-266, 1997.
DOI : 10.1111/j.2044-8317.1993.tb01005.x

B. Le-roux, Multiple Correspondence Analysis, SAGE publications, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00625919

J. Li and D. Tao, Simple exponential family PCA, Neural Networks and Learning Systems IEEE Transactions on, vol.24, issue.3, pp.485-497, 2013.

R. J. Little and D. B. Rubin, Statistical Analysis with Missing Data Wiley series in probability and statistics, 1987.

G. Michailidis and J. Leeuw, The Gifi system of descriptive multivariate analysis, Statistical Science, vol.13, issue.4, pp.307-336, 1998.
DOI : 10.1214/ss/1028905828

S. Nishisato, Analysis of Categorical Data: Dual Scaling and its Applications, 1980.

D. B. Rubin, Multiple Imputation for Non-Response in Survey, 1987.

A. Andrey, . Shabalin, B. Andrew, and . Nobel, Reconstruction of a low-rank matrix in the presence of Gaussian noise, Journal of Multivariate Analysis, vol.118, pp.67-76, 2013.

N. Srebro, Learning with Matrix Factorizations, 2004.

M. Tenenhaus and F. W. Young, An analysis and synthesis of multiple correspondence analysis, optimal scaling, dual scaling, homogeneity analysis and other methods for quantifying categorical multivariate data, Psychometrika, vol.25, issue.2, pp.91-119, 1985.
DOI : 10.1111/j.2044-8317.1953.tb00126.x

R. Tibshirani, Regression shrinkage and selection via the Lasso, Journal of the Royal Statistical Society, Series B: Methodological, vol.58, pp.267-288, 1996.

R. J. Tibshirani and J. Taylor, Degrees of freedom in lasso problems. The Annals of Statistics, pp.1198-1232, 2012.

S. Van-buuren, Flexible Imputation of Missing Data (Chapman & Hall/CRC Interdisciplinary Statistics) Chapman and Hall/CRC, 2012.

H. Zou, T. Hastie, and R. Tibshirani, On the ???degrees of freedom??? of the lasso, The Annals of Statistics, vol.35, issue.5, pp.2173-2192, 2007.
DOI : 10.1214/009053607000000127

A. Agresti, Categorical Data Analysis, 2013.

V. Audigier, F. Husson, and J. Josse, A principal components method to impute missing values for mixed data Advances in Data Analysis and Classification, pp.5-26, 2014.

V. Audigier, F. Husson, and J. Josse, Multiple imputation for continuous variables using a Bayesian principal component analysis, Journal of Statistical Computation and Simulation, vol.45, issue.3, 2014.
DOI : 10.1201/b17700
URL : https://hal.archives-ouvertes.fr/hal-00951915

V. Audigier, F. Husson, and J. Josse, MIMCA: multiple imputation for categorical variables with multiple correspondence analysis, Statistics and Computing, vol.62, issue.38, 2015.
DOI : 10.1198/000313008X300912
URL : https://hal.archives-ouvertes.fr/hal-01170864

P. Baldi and K. Hornik, Neural networks and principal component analysis: Learning from examples without local minima, Neural Networks, vol.2, issue.1, pp.53-58, 1989.
DOI : 10.1016/0893-6080(89)90014-2

D. Bartholomew, Latent Variable Models and Factor Analysis, 1987.
DOI : 10.1002/9781119970583

D. Bates and D. Watt, Relative curvature measure of nonlinearity, Journal of the Royal Society series B, vol.42, pp.1-25, 1980.

J. Benzécri, L'analyse des données. Tome II: L'analyse des correspondances, 1973.

J. Besag, Spatial Interaction and the Statistical Analysis of Lattice Systems, Journal of the Royal Statistical Society. Series B (Methodological), vol.36, issue.2, 1974.

P. Besse and A. De-falguerolles, Application of Resampling Methods to the Choice of Dimension in Principal Component Analysis, Computer Intensive Methods in Statistics, pp.167-176, 1993.
DOI : 10.1007/978-3-642-52468-4_11

C. Bishop, Training with Noise is Equivalent to Tikhonov Regularization, Neural Computation, vol.1, issue.1, pp.108-116, 1995.
DOI : 10.1162/neco.1994.6.1.147
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.38.3008

H. Bourlard and Y. Kamp, Auto-association by multilayer perceptrons and singular value decomposition, Biological Cybernetics, vol.13, issue.4-5, pp.4-5, 1988.
DOI : 10.1109/MASSP.1987.1165576
URL : https://infoscience.epfl.ch/record/82601/files/rr00-16.pdf

J. Cai, E. Candès, and Z. Shen, A Singular Value Thresholding Algorithm for Matrix Completion, SIAM Journal on Optimization, vol.20, issue.4, pp.1956-1982, 2010.
DOI : 10.1137/080738970

E. Candès, C. Sing-long, and J. Trzasko, Unbiased Risk Estimates for Singular Value Thresholding and Spectral Estimators, IEEE Transactions on Signal Processing, vol.61, issue.19, pp.61-4643, 2013.
DOI : 10.1109/TSP.2013.2270464

E. Candes, C. Sing-long, and J. Trzasko, Unbiased Risk Estimates for Singular Value Thresholding and Spectral Estimators, IEEE Transactions on Signal Processing, vol.61, issue.19, pp.61-4643, 2013.
DOI : 10.1109/TSP.2013.2270464
URL : http://arxiv.org/abs/1210.4139

E. Candès and T. Tao, The Power of Convex Relaxation: Near-Optimal Matrix Completion, IEEE Transactions on Information Theory, vol.56, issue.5, pp.2053-2080, 2009.
DOI : 10.1109/TIT.2010.2044061

J. Carpenter and M. Kenward, Multiple Imputation and its Application, 2013.
DOI : 10.1002/9781119942283

H. Caussinus, Models and Uses of Principal Component Analysis (with Discussion), Multidimensional Data Analysis, pp.149-178, 1986.

Y. Chikuse, Statistics on Special Manifolds, 2003.
DOI : 10.1007/978-0-387-21540-2

R. Christensen, Log-Linear Models, 2010.
DOI : 10.1007/978-1-4757-4111-7

C. Christiansen and C. Morris, Hierarchical Poisson Regression Modeling, Journal of the American Statistical Association, vol.42, issue.438, pp.618-632, 1997.
DOI : 10.2307/2531248

P. Cornelius, J. Crossa, and M. Seyedsadr, Statistical tests and estimators of multiplicative models for genotype by environment interaction, Genotype by environment interaction, pp.199-234, 1996.

P. Craven and G. Wahba, Smoothing noisy data with spline functions, Numerische Mathematik, vol.4, issue.4, pp.377-403, 1979.
DOI : 10.1214/aoms/1177697089

J. Daudin, C. Duby, and P. Trecourt, Pca stability studied by the bootstrap and the infinitesimal jackknife method, Statistics, vol.63, issue.2, pp.255-270, 1989.
DOI : 10.1093/biomet/67.1.45

A. De-falguerolles, Log-Bilinear Biplots in Action, Visualisation Of Categorical Data, pp.527-533, 1998.
DOI : 10.1016/B978-012299045-8/50039-5

D. Leeuw and J. , Gifi goes logistic, 2005.

J. De-leeuw and J. Rijckevorsel, HOMALS and PRINCALS -Some generalizations of principal components analysis, Data analysis and informatics, pp.231-242, 1980.

M. De-tayrac, S. Lê, M. Aubry, J. Mosser, and F. Husson, Simultaneous analysis of distinct Omics data sets with integration of biological knowledge: Multiple Factor Analysis approach., BMC Genomics, vol.10, issue.1, p.32, 2009.
DOI : 10.1186/1471-2164-10-32
URL : https://hal.archives-ouvertes.fr/inserm-00365978

A. Dempster, N. Laird, and D. Rubin, Maximum Likelihood from Incomplete Data via the EM Algorithm, Journal of the Royal Statistical Society B, vol.39, issue.1, pp.1-38, 1977.

J. Denis and J. Gower, Asymptotic covariances for the parameters of biadditive models, Utilitas Mathematica, pp.193-205, 1994.

J. Denis and J. Gower, Asymptotic Confidence Regions for Biadditive Models: Interpreting Genotype- Environment Interactions, Applied Statistics, vol.45, issue.4, pp.479-493, 1996.
DOI : 10.2307/2986069

J. Denis and A. Pazman, Bias of least squares estimators in nonlinear regression models with constraints. Part II: Biadditive Models, Applications of Mathematics, vol.44, pp.359-374, 1999.

S. Dray and J. Josse, Principal component analysis with missing values: a comparative survey of methods, Plant Ecology, vol.64, issue.10, pp.657-667, 2014.
DOI : 10.1348/000711010X497442
URL : https://hal.archives-ouvertes.fr/hal-01260054

C. Eckart and G. Young, The approximation of one matrix by another of lower rank, Psychometrika, vol.1, issue.3, pp.211-218, 1936.
DOI : 10.1007/BF02288367

B. Efron and C. Morris, Limiting the risk of Bayes and empirical Bayes estimators. Part II: The empirical Bayes case, Journal of the American Statistical Association, vol.67, issue.19, pp.130-139, 1972.

B. Efron and C. Stein, The Jackknife Estimate of Variance, Annals of Statistics, vol.3, pp.586-596, 1981.

B. Efron and R. Tibshirani, An Introduction to the Bootstrap, 1994.
DOI : 10.1007/978-1-4899-4541-9

B. Escofier, Traitement Simultané de Variables Quantitatives et Qualitatives en Analyse Factorielle, Les cahiers de l'analyse des données, pp.137-146, 1979.

B. Escofier and J. Pagès, Analyses Factorielles Simples et Multiples, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00382085

H. Gauch, Model Selection and Validation for Yield Trials with Interaction, Biometrics, vol.44, issue.3, pp.705-715, 1988.
DOI : 10.2307/2531585

H. Gauch and R. Zobel, AMMI analysis of yield trials In Genotype by environment interaction, pp.141-150, 1996.

M. Gavish and D. Donoho, Optimal Shrinkage of Singular Values, IEEE Transactions on Information Theory, vol.63, issue.4, 2014.
DOI : 10.1109/TIT.2017.2653801

A. Gelman and J. Hill, Data Analysis Using Regression and Multilevel/Hierarchical Models, 2007.
DOI : 10.1017/CBO9780511790942

C. Giacobino, S. Sardy, D. Rodriguez, J. Hengartner, and N. , Quantile universal threshold for model selection, 2015.

A. Gifi, Non-linear Multivariate Analysis, 1990.

A. Gifi, Nonlinear Multivariate Analysis, 1990.

J. Gower, S. Lubbe, L. Roux, and N. , Understanding Biplots, 2011.
DOI : 10.1002/9780470973196

J. Gower and G. Dijksterhuis, Procrustes Problems, 2004.
DOI : 10.1093/acprof:oso/9780198510581.001.0001

M. Greenacre, Theory and Applications of Correspondence Analysis, 1984.

M. Greenacre, Biplots in Practice. Fundacion BBVA (FBBVA), 2009.

M. Greenacre and J. Blasius, Multiple Correspondence Analysis and Related Methods, 2006.
DOI : 10.1201/9781420011319

M. Greenacre, Theory and Applications of Correspondence Analysis, 1984.

M. Greenacre, Correspondence Analysis in Practice, 2007.

P. Groenen and J. Josse, Multinomial MCA, 2016.

P. Hoff, Simulation of the Matrix Bingham???von Mises???Fisher Distribution, With Applications to Multivariate and Relational Data, Journal of Computational and Graphical Statistics, vol.18, issue.2, pp.438-456, 2009.
DOI : 10.1198/jcgs.2009.07177

J. Honaker, G. King, and M. Blackwell, Amelia II: A Program for Missing Data, Journal of Statistical Software, issue.7, pp.45-46, 2011.

J. Honaker, G. King, and M. Blackwell, Amelia II: A Program for Missing Data, 2014.

S. Huet, J. Denis, and K. Adamczyk, Bootstrap Confidence Intervals In Nonlinear Regression Models When The Number of Observations is Fixed and The Variance Tends To 0. Application To Biadditive Models, Statistics, vol.18, issue.3, pp.203-227, 1999.
DOI : 10.1016/0047-259X(86)90069-2

F. Husson and J. Josse, Handling missing values in multiple factor analysis, Food Quality and Preference, vol.30, issue.2, pp.77-85, 2013.
DOI : 10.1016/j.foodqual.2013.04.013
URL : https://hal.archives-ouvertes.fr/hal-01070888

F. Husson and J. Josse, Multiple Correspondence Analysis Visualization and Verbalization of Data, pp.163-181, 2014.

F. Husson and J. Josse, Multiple Correspondence Analysis (MCA), Visualization and Verbalization of Data, pp.165-184, 2014.
DOI : 10.1201/b10345-4

F. Husson and J. Josse, missMDA: Handling Missing Values with Multivariate Data Analysis. R package version 1.9, URL http, 2015.

F. Husson, J. Josse, and G. Saporta, Jan de Leeuw and the French School of Data Analysis, Journal of Statistical Software, vol.73, issue.6, 2016.
DOI : 10.18637/jss.v073.i06
URL : https://hal.archives-ouvertes.fr/hal-01400295

F. Husson, S. Le, and J. Pagès, Exploratory Multivariate Analysis by Example Using R, 2010.
DOI : 10.1201/b10345
URL : https://hal.archives-ouvertes.fr/hal-00566638

S. Ivanoff, F. Picard, and V. Rivoirard, Adaptive Lasso and group-Lasso for functional Poisson regression, The Journal of Machine Learning Research, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01097914

J. Josse, M. Chavent, B. Liquet, and F. Husson, Handling Missing Values with Regularized Iterative Multiple Correspondence Analysis, Journal of Classification, vol.33, issue.1, pp.91-116, 2012.
DOI : 10.1111/j.1467-9531.2008.00202.x
URL : https://hal.archives-ouvertes.fr/hal-00647378

J. Josse and S. Holmes, Test of independence and beyond, 2015.

J. Josse and F. Husson, Multiple Imputation in PCA Advances in data analysis and classification, pp.231-246, 2011.

J. Josse and F. Husson, Selecting the number of components in principal component analysis using cross-validation approximations, Computational Statistics & Data Analysis, vol.56, issue.6, pp.1869-1879, 2011.
DOI : 10.1016/j.csda.2011.11.012

J. Josse and F. Husson, Handling missing values in exploratory multivariate data analysis methods, Journal de la Société Française de Statistique, pp.79-99, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00811888

J. Josse and F. Husson, missMDA a package to handle missing values in and with multivariate data analysis methods, Journal of Statistical Software, 2015.

J. Josse, F. Husson, and S. Wager, Confidence Areas for Fixed-Effects PCA, Journal of Computational and Graphical Statistics, vol.53, issue.1, 2014.
DOI : 10.2135/cropsci2013.04.0218
URL : https://hal.archives-ouvertes.fr/hal-01059057

J. Josse, J. Pagès, and F. Husson, Gestion des Données Manquantes en Analyse en Composantes Principales, Journal de la Société Française de Statistique, pp.28-51, 2009.

J. Josse, S. Sardy, and S. Wager, denoiseR: a package for low rank matrix estimation, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01278417

J. Josse, M. Timmerman, H. Kiers, and A. Smilde, Missing values in multi-level simultaneous component analysis, Chemometrics and Intelligent Laboratory Systems, vol.129, issue.2, pp.21-32, 2013.
DOI : 10.1016/j.chemolab.2013.05.010
URL : https://hal.archives-ouvertes.fr/hal-01070880

J. Josse, F. Van-eeuwijk, H. Piepho, and J. Denis, Another Look at Bayesian Analysis of AMMI Models for Genotype-Environment Data, Journal of Agricultural, Biological, and Environmental Statistics, vol.84, issue.3, pp.240-257, 2014.
DOI : 10.1016/S0378-3758(99)00151-2
URL : https://hal.archives-ouvertes.fr/hal-01111495

J. Josse and S. Wager, Stable Autoencoding: A Flexible Framework for Regularized Low-rank Matrix Estimation, Procedia Computer Science, vol.51, 2014.
DOI : 10.1016/j.procs.2015.05.420
URL : https://hal.archives-ouvertes.fr/hal-01148810

J. Josse and S. Wager, Stable Autoencoding: A Flexible Framework for Regularized Low-rank Matrix Estimation, Procedia Computer Science, vol.51, 2015.
DOI : 10.1016/j.procs.2015.05.420
URL : https://hal.archives-ouvertes.fr/hal-01148810

J. Josse, S. Wager, and S. Sardy, denoiseR: Regularized low-rank matrix estimation, 2015.

C. Khatri and K. Mardia, The Von Mises-Fisher Matrix Distribution in Orientation Statistics, Journal of the Royal Statistical Society. Series B, vol.39, issue.1, pp.95-106, 1977.

H. Kiers, Simple structure in component analysis techniques for mixtures of qualitative and quantitative variables, Psychometrika, vol.50, issue.2, pp.197-212, 1991.
DOI : 10.1007/BF02294458

H. Kiers, Weighted least squares fitting using ordinary least squares algorithms, Psychometrika, vol.18, issue.2, pp.251-266, 1997.
DOI : 10.1111/j.2044-8317.1993.tb01005.x

Y. Koren, R. Bell, and C. Volinsky, Matrix Factorization Techniques for Recommender Systems, Computer, vol.42, issue.8, pp.30-37, 2009.
DOI : 10.1109/MC.2009.263
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.147.8295

P. Kroonenberg, Applied Multiway Data Analysis (chap.7), series in probability and statistics, 2008.
DOI : 10.1002/9780470238004

J. Kropko, B. Goodrich, A. Gelman, and J. Hill, Multiple Imputation for Continuous and Categorical Data: Comparing Joint and Conditional Approaches, Political Analysis, 2014.

J. Kropko, B. Goodrich, A. Gelman, and J. Hill, Multiple Imputation for Continuous and Categorical Data: Comparing Joint Multivariate Normal and Conditional Approaches, Political Analysis, vol.9, issue.04, 2014.
DOI : 10.1080/02664760902744954

W. Krzanowski, Principles of multivariate analysis; a user's perspective, 2010.

P. Lazarsfeld and N. Henry, Latent Structure Analysis, 1968.

S. Lê, J. Josse, and F. Husson, FactoMineR: An R Package for Multivariate Analysis, Journal of Statistical Software, vol.25, issue.1, pp.1-18, 2008.

L. Lebart, Which Bootstrap for Principal Axes Methods?, Selected Contributions in Data Analysis and Classification, pp.581-588, 2007.
DOI : 10.1007/978-3-540-73560-1_55

L. Lebart and G. Saporta, Historical Elements of Correspondence Analysis and Multiple Correspondence Analysis, Visualization and Verbalization of Data, pp.31-44, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01126409

J. Leek and J. Storey, Capturing Heterogeneity in Gene Expression Studies by Surrogate Variable Analysis, PLoS Genetics, vol.3, issue.9, p.161, 2007.
DOI : 10.1371/journal.pgen.0030161.sg011

R. Little and D. Rubin, Statistical Analysis with Missing Data, series in probability and statistics, 1987.
DOI : 10.1002/9781119013563

M. Lustig, D. Donoho, J. Santos, and J. Pauly, Compressed Sensing MRI, IEEE Signal Processing Magazine, vol.25, issue.2, pp.72-82, 2008.
DOI : 10.1109/MSP.2007.914728

P. Martyn, JAGS: A Program for Analysis of Bayesian Graphical Models Using Gibbs Sampling, Proceedings of the 3rd International Workshop on Distributed Statistical Computing, 2003.

X. Meng and D. Rubin, Using EM to Obtain Asymptotic Variance-Covariance Matrices: The SEM Algorithm, Journal of the American Statistical Association, vol.82, issue.416, pp.899-909, 1991.
DOI : 10.1002/9780470316696

G. Michailidis and J. De-leeuw, The Gifi system of descriptive multivariate analysis, Statistical Science, vol.13, issue.4, pp.307-336, 1998.
DOI : 10.1214/ss/1028905828

K. Mosler, Depth Statistics, Robustness and Complex Data Struc-tures, Festschrift in Honour of Ursula Gather, pp.17-34, 2013.
DOI : 10.1007/978-3-642-35494-6_2

J. Pagès, Multiple Factor Analysis with R, 2015.

T. Papadopoulo and M. Lourakis, Estimating the Jacobian of the Singular Value Decomposition: Theory and Applications, Proceedings of the European Conference on Computer Vision, ECCV00, pp.554-570, 2000.
DOI : 10.1007/3-540-45054-8_36
URL : https://hal.archives-ouvertes.fr/inria-00072686

A. Pazman, Results on nonlinear least squares estimators under nonlinear equality constraints, Journal of Statistical Planning and Inference, vol.103, issue.1-2, pp.401-420, 2002.
DOI : 10.1016/S0378-3758(01)00234-8

A. Pazman and J. Denis, Measures of nonlinearity for a biadditive ANOVA model, Metrika, vol.55, issue.3, pp.233-245, 2002.
DOI : 10.1007/s001840100144

S. Perez-elizalde, D. Jarquin, and J. Crossa, A General Bayesian Estimation Method of Linear???Bilinear Models Applied to Plant Breeding Trials With Genotype ?? Environment Interaction, Journal of Agricultural, Biological, and Environmental Statistics, vol.84, issue.1, pp.15-37, 2011.
DOI : 10.1016/S0378-3758(99)00151-2

A. Price, N. Patterson, R. Plenge, M. Weinblatt, N. Shadick et al., Principal components analysis corrects for stratification in genome-wide association studies, Nature Genetics, vol.15, issue.8, pp.38-904, 2006.
DOI : 10.1111/j.1469-1809.1949.tb02451.x

G. Robinson, That BLUP is a Good Thing: The Estimation of Random Effects, Statistical Science, vol.6, issue.1, pp.15-32, 1991.
DOI : 10.1214/ss/1177011926

C. Royo, A. Rodriguez, and I. Romagosa, Differential Adaptation of Complete and Substituted Triticale, Plant Breeding, vol.80, issue.2, pp.113-119, 1993.
DOI : 10.1007/BF00040364

D. Rubin, Inference and missing data, Biometrika, vol.63, issue.3, pp.581-592, 1976.
DOI : 10.1093/biomet/63.3.581

D. Rubin, Multiple Imputation for Non-Response in Survey, 1987.

J. Schafer, Analysis of incomplete multivariate data, 1997.
DOI : 10.1201/9781439821862

P. Schoenemann, A generalized solution of the orthogonal procrustes problem, Psychometrika, vol.22, issue.1, pp.1-10, 1966.
DOI : 10.1007/BF02289451

A. Shabalin and A. Nobel, Reconstruction of a low-rank matrix in the presence of Gaussian noise, Journal of Multivariate Analysis, vol.118, pp.67-76, 2013.
DOI : 10.1016/j.jmva.2013.03.005

Y. Si and J. Reiter, Nonparametric Bayesian Multiple Imputation for Incomplete Categorical Variables in Large-Scale Assessment Surveys, Journal of Educational and Behavioral Statistics, vol.38, issue.5, pp.499-521, 2013.
DOI : 10.3102/1076998613480394

S. Silvey, Statistical Inference., Applied Statistics, vol.25, issue.3, 1975.
DOI : 10.2307/2347253

V. Smidl and A. Quinn, On Bayesian principal component analysis, Computational Statistics & Data Analysis, vol.51, issue.9, pp.4101-4123, 2007.
DOI : 10.1016/j.csda.2007.01.011

C. Stein, Estimation of the Mean of a Multivariate Normal Distribution, The Annals of Statistics, vol.9, issue.6, pp.1135-1151, 1981.
DOI : 10.1214/aos/1176345632

D. Stekhoven and P. Bühlmann, MissForest -Nonparametric missing value imputation for mixed-type data, Bioinformatics, vol.28, pp.113-118, 2012.
DOI : 10.1093/bioinformatics/btr597
URL : http://arxiv.org/abs/1105.0828

Y. Takane, Constrained Principal Component Analysis and Related Techniques, 2013.

M. Tanner and W. Wong, The Calculation of Posterior Distributions by Data Augmentation, Journal of the American Statistical Association, vol.56, issue.398, pp.805-811, 1987.
DOI : 10.1016/0304-4076(84)90007-1

M. Templ, A. Alfons, A. Kowarik, and B. Prantner, VIM: Visualization and Imputation of Missing Values. R package version 4.0.0, URL http, 2013.

R. Tibshirani, Regression shrinkage and selection via the lasso, Journal of the Royal Statistical Society. Series B, pp.267-288, 1996.
DOI : 10.1111/j.1467-9868.2011.00771.x

R. Tibshirani, Regression shrinkage and selection via the Lasso, Journal of the Royal Statistical Society, Series B: Methodological, vol.58, pp.267-288, 1996.
DOI : 10.1111/j.1467-9868.2011.00771.x

S. Van-buuren, Multiple imputation of discrete and continuous data by fully conditional specification, Statistical Methods in Medical Research, vol.4, issue.1, pp.219-242, 2007.
DOI : 10.22237/jmasm/1114907160

S. Van-buuren, &. Chapman, /. Hall, B. Crc, and . Raton, Flexible Imputation of Missing Data, 2012.
DOI : 10.1201/b11826

S. Van-buuren, H. Boshuizen, and D. Knook, Multiple imputation of missing blood pressure covariates in survival analysis, Statistics in Medicine, vol.142, issue.6, pp.681-694, 1999.
DOI : 10.1007/978-1-4684-0192-9

M. Verbanck, J. Josse, and F. Husson, Regularized PCA to Denoise and Visualise Data, Statistics and Computing, pp.1-16, 2013.
DOI : 10.1007/s11222-013-9444-y
URL : http://arxiv.org/abs/1301.4649

J. Vermunt, J. Van-ginkel, L. Van-der-ark, and K. Sijtsma, 9. Multiple Imputation of Incomplete Categorical Data Using Latent Class Analysis, Sociological Methodology, vol.41, issue.12, pp.369-397, 2008.
DOI : 10.1016/S0167-9473(02)00179-2

D. Vidotto, M. Kapteijn, and J. Vermunt, Multiple imputation of missing categorical data using latent class models: State of art Psychological Test and Assessment Modeling, 2014.

K. Viele and C. Srinivasan, Parsimonious estimation of multiplicative interaction in analysis of variance using Kullback???Leibler Information, Journal of Statistical Planning and Inference, vol.84, issue.1-2, pp.201-219, 2000.
DOI : 10.1016/S0378-3758(99)00151-2

S. Wager, W. Fithian, S. Wang, and P. Liang, Altitude Training: Strong Bounds for Single-Layer Dropout, Advances in Neural Information Processing Systems, 2014.

H. Wold and E. Lyttkens, Nonlinear iterative partial least squares (NIPALS) estimation procedures, Bulletin. Int. Stat. Institut, vol.43, pp.29-51, 1969.

C. Zhang and J. Huang, The sparsity and bias of the Lasso selection in high-dimensional linear regression, The Annals of Statistics, vol.36, issue.4, pp.1567-1594, 2008.
DOI : 10.1214/07-AOS520

H. Zou, The Adaptive Lasso and Its Oracle Properties, Journal of the American Statistical Association, vol.101, issue.476, pp.1418-1429, 2006.
DOI : 10.1198/016214506000000735