J. M. Aza¨?saza¨?s, C. Delmas, and C. E. Rabier, Likelihood ratio test process for quantitative trait locus detection, Statistics, vol.138, issue.1, pp.787-801, 2014.
DOI : 10.1023/A:1009683603862

J. C. Barrett, S. Hansoul, D. L. Nicolae, J. H. Cho, R. H. Duerr et al., Genome-wide association defines more than 30 distinct susceptibility loci for Crohn's disease. Nature genetics, pp.40-955, 2008.

E. S. Buckler, J. B. Holland, P. J. Bradbury, C. B. Acharya, P. J. Brown et al., The Genetic Architecture of Maize Flowering Time, Science, vol.325, issue.5941, pp.325-714, 2009.
DOI : 10.1126/science.1174276

P. Bühlmann, Statistical significance in high-dimensional linear models, Bernoulli, vol.19, issue.4, pp.1212-1242, 2013.
DOI : 10.3150/12-BEJSP11

J. Burstin, P. Salloignon, M. Martinello, J. B. Magnin-robert, M. Siol et al., Genetic diversity and trait genomic prediction in a pea diversity panel, BMC Genomics, vol.16, issue.1, p.105, 2015.
DOI : 10.1007/BF00015981

T. T. Cai, C. Zhang, and H. H. Zhou, Optimal rates of convergence for covariance matrix estimation, The Annals of Statistics, vol.38, issue.4, pp.2118-2144, 2010.
DOI : 10.1214/09-AOS752

M. N. Chang, R. Wu, S. S. Wu, and G. Casella, Score statistics for mapping quantitative trait loci. Statistical applications in genetics and molecular biology, pp.1-35, 2009.
DOI : 10.2202/1544-6115.1386
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.111.2782

Z. Chen and H. Chen, On some statistical aspects of the interval mapping for QTL detection, Statistica Sinica, vol.15, issue.4, pp.909-925, 2005.

C. Cierco, Asymptotic Distribution of the Maximum Likelihood Ratio Test for Gene Detection, Statistics, vol.138, issue.3, pp.261-285, 1998.
DOI : 10.2307/2533317

R. R. Corbeil and S. R. Searle, Restricted Maximum Likelihood (REML) Estimation of Variance Components in the Mixed Model, Technometrics, vol.18, issue.1, pp.31-38, 1976.
DOI : 10.2307/1267913

H. D. Daetwyler, B. Villanueva, and J. A. Woolliams, Accuracy of Predicting the Genetic Risk of Disease Using a Genome-Wide Approach, PLoS ONE, vol.5, issue.10, p.3395, 2008.
DOI : 10.1371/journal.pone.0003395.s002

H. D. Daetwyler, B. Villanueva, and J. A. Woolliams, The Impact of Genetic Architecture on Genome-Wide Evaluation Methods, Genetics, vol.185, issue.3, pp.1021-1031, 2010.
DOI : 10.1534/genetics.110.116855

L. H. Dicker, Ridge regression and asymptotic minimax estimation over spheres of growing dimension, Bernoulli, vol.22, issue.1, pp.1-37, 2016.
DOI : 10.3150/14-BEJ609

R. Durrett, Probability models for DNA sequence evolution, 2008.

J. B. Endelman, Ridge regression and other kernels for genomic selection with R package rrBLUP. The Plant Genome, pp.250-255, 2011.
DOI : 10.3835/plantgenome2011.08.0024

J. Fan and J. Lv, Sure independence screening for ultrahigh dimensional feature space, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.36, issue.5, pp.849-911, 2008.
DOI : 10.1111/j.1467-9868.2008.00674.x
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2709408

J. Friedman, T. Hastie, and R. Tibshirani, The elements of statistical learning, 2001.

M. E. Goddard and B. J. Hayes, Mapping genes for complex traits in domestic animals and their use in breeding programmes, Nature Reviews Genetics, vol.39, issue.6, pp.381-391, 2009.
DOI : 10.1038/nrg2575

M. Goddard, Genomic selection: prediction of accuracy and maximisation of long term response, Genetica, vol.169, issue.2, pp.245-257, 2009.
DOI : 10.1007/s10709-008-9308-0

M. E. Goddard, B. J. Hayes, and T. H. Meuwissen, Using the genomic relationship matrix to predict the accuracy of genomic selection, Journal of Animal Breeding and Genetics, vol.42, issue.6, pp.409-421, 2011.
DOI : 10.1111/j.1439-0388.2011.00964.x

A. Goldenshluger and A. Tsybakov, Optimal prediction for linear regression with infinitely many parameters, Journal of Multivariate Analysis, vol.84, issue.1, pp.40-60, 2003.
DOI : 10.1016/S0047-259X(02)00006-4
URL : https://hal.archives-ouvertes.fr/hal-00103951

B. Hayes, P. Bowman, A. Chamberlain, and M. Goddard, Invited review: Genomic selection in dairy cattle: Progress and challenges, Journal of Dairy Science, vol.92, issue.2, pp.433-443, 2009.
DOI : 10.3168/jds.2008-1646

J. L. Jannink, A. J. Lorenz, and H. Iwata, Genomic selection in plant breeding: from theory to practice, Briefings in Functional Genomics, vol.9, issue.2, pp.166-177, 2010.
DOI : 10.1093/bfgp/elq001

H. P. Kärkkäinen and M. J. Sillanpää, Back to Basics for Bayesian Model Building in Genomic Selection, Genetics, vol.191, issue.3, pp.969-987, 2012.
DOI : 10.1534/genetics.112.139014

D. Y. Kim, Y. Cui, and O. Zhao, Asymptotic test of mixture model and its applications to QTL interval mapping, Journal of Statistical Planning and Inference, vol.143, issue.8, pp.1320-1329, 2009.
DOI : 10.1016/j.jspi.2013.03.020

S. Kumar, D. Chagné, M. C. Bink, R. K. Volz, C. Whitworth et al., Genomic selection for fruit quality traits in apple (Malus× domestica Borkh.). PloS One, p.36674, 2012.

D. Habier, R. Fernando, and J. Dekkers, The impact of genetic relationship information on genome-assisted breeding values, Genetics, vol.177, issue.4, pp.2389-2397, 2007.
DOI : 10.1534/genetics.107.081190

J. Haldane, The combination of linkage values and the calculation of distances between the loci of linked factors, J Genet, vol.8, issue.29, pp.299-309, 1919.

W. Hill and B. Weir, Variances and covariances of squared linkage disequilibria in finite populations. Theoretical population biology, pp.54-78, 1998.

A. E. Hoerl and R. W. Kennard, Ridge Regression: Biased Estimation for Nonorthogonal Problems, Technometrics, vol.24, issue.1, pp.55-67, 1970.
DOI : 10.2307/1909769

E. S. Lander and D. Botstein, Mapping mendelian factors underlying quantitative traits using RFLP linkage maps, Genetics, vol.121, issue.1, pp.185-199, 1989.

J. Li and L. Ji, Adjusting multiple testing in multilocus analyses using the eigenvalues of a correlation matrix, Heredity, vol.62, issue.3, pp.221-227, 2005.
DOI : 10.1002/1098-2272(200012)19:4<323::AID-GEPI4>3.0.CO;2-5

Z. Li and M. J. Sillanpää, Overview of LASSO-related penalized regression methods for quantitative trait mapping and genomic selection, Theoretical and Applied Genetics, vol.35, issue.3, pp.419-435, 2012.
DOI : 10.1007/s00122-012-1892-9

M. Lynch and B. Walsh, Genetics and analysis of quantitative traits, 1998.

T. H. Meuwissen, B. Hayes, and M. E. Goddard, Prediction of total genetic value using genome-wide dense marker maps, Genetics, vol.157, issue.4, pp.1819-1829, 2001.

C. E. Rabier, P. Barre, T. Asp, G. Charmet, and B. Mangin, On the Accuracy of Genomic Selection, PLOS ONE, vol.112, issue.6, 2016.
DOI : 10.1371/journal.pone.0156086.s004

T. Schulz-streeck, J. Ogutu, Z. Karaman, C. Knaak, and H. Piepho, Genomic Selection using Multiple Populations, Crop Science, vol.52, issue.6, pp.2453-2461, 2012.
DOI : 10.2135/cropsci2012.03.0160

J. Shao and X. Deng, Estimation in high-dimensional linear models with deterministic design matrices. The Annals of Statistics, pp.812-831, 2012.

J. Spindel, H. Begum, D. Akdemir, P. Virk, B. Collard et al., Genomic Selection and Association Mapping in Rice (Oryza sativa): Effect of Trait Genetic Architecture, Training Population Composition, Marker Number and Statistical Model on Accuracy of Rice Genomic Selection in Elite, Tropical Rice Breeding Lines, PLOS Genetics, vol.45, issue.2, p.1004982, 2015.
DOI : 10.1371/journal.pgen.1004982.s011

J. E. Spindel, H. Begum, D. Akdemir, B. Collard, E. Redoña et al., Genome-wide prediction models that incorporate de novo GWAS are a powerful new tool for tropical rice improvement, Heredity, vol.127, issue.4, pp.395-408, 2016.
DOI : 10.1038/ng.2310

F. Technow, R Package hypred: Simulation of Genomic Data in Applied Genetics Available from: ??? 06, 2014.

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

A. N. Tikhonov, On the solution of ill-posed problems and the method of regularization, Dokl. Akad. Nauk.. SSSR, vol.151, pp.501-504, 1963.

P. M. Visscher, J. Yang, M. E. Goddard, and . Yang, A Commentary on ???Common SNPs Explain a Large Proportion of the Heritability for Human Height??? by Yang et al. (2010), Twin Research and Human Genetics, vol.460, issue.06, pp.517-524, 2010.
DOI : 10.1038/ng.608

M. N. Weedon, H. Lango, C. M. Lindgren, C. Wallace, D. M. Evans et al., Genome-wide association analysis identifies 20 loci that influence adult height. Nature genetics, pp.40-575, 2008.
DOI : 10.1038/ng.121
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2681221

R. Wu, C. Ma, and G. Casella, Statistical genetics of quantitative traits: linkage, maps and QTL, 2007.

T. Würschum, J. C. Reif, T. Kraft, G. Janssen, and Y. Zhao, Genomic selection in sugar beet breeding populations, BMC Genetics, vol.14, issue.1, p.85, 2013.
DOI : 10.1111/j.1439-0388.2007.00701.x

M. Yuan and Y. Lin, Model selection and estimation in regression with grouped variables, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.58, issue.1, pp.49-67, 2006.
DOI : 10.1198/016214502753479356

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
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.649.404

R. Rabier, C. E. Barre, P. Asp, T. Charmet, G. Mangin et al., On the Accuracy of Genomic Selection, PLOS ONE, vol.112, issue.6, 2016.
DOI : 10.1371/journal.pone.0156086.s004