W. F. Hoeffding, A Class of Statistics with Asymptotically Normal Distribution, The Annals of Mathematical Statistics, vol.19, issue.3, pp.293-325, 1948.
DOI : 10.1214/aoms/1177730196

F. Gamboa, A. Janon, T. Klein, A. Lagnoux, and C. Prieur, Statistical inference for Sobol pick-freeze Monte Carlo method, Statistics, vol.89, issue.4, pp.881-902, 2016.
DOI : 10.4213/tvp3534
URL : https://hal.archives-ouvertes.fr/hal-00804668

M. D. Mckay, Evaluating prediction uncertainty, pp.1-79, 1995.
DOI : 10.2172/29432

J. Tissot and C. Prieur, A randomized orthogonal array-based procedure for the estimation of first- and second-order Sobol' indices, Journal of Statistical Computation and Simulation, vol.3, issue.2, pp.1358-1381, 2015.
DOI : 10.1214/aos/1069362310
URL : https://hal.archives-ouvertes.fr/hal-00743964

T. A. Mara and O. Joseph, Comparison of some efficient methods to evaluate the main effect of computer model factors, Journal of Statistical Computation and Simulation, vol.1, issue.2, pp.167-178, 2008.
DOI : 10.1016/S0378-7788(00)00127-4
URL : https://hal.archives-ouvertes.fr/hal-01093033

G. Archer, A. Saltelli, and I. Sobol, Sensitivity measures,anova-like Techniques and the use of bootstrap, Journal of Statistical Computation and Simulation, vol.2, issue.2, pp.99-120, 1997.
DOI : 10.1142/S0129183195000204

A. Saltelli, Making best use of model evaluations to compute sensitivity indices, Computer Physics Communications, vol.145, issue.2, pp.280-297, 2002.
DOI : 10.1016/S0010-4655(02)00280-1

A. Owen, H. Monod, C. Naud, and D. Makowski, Lattice sampling revisited: Monte carlo variance of means over randomized orthogonal arrays Uncertainty and sensitivity analysis for crop models, Working with Dynamic Crop Models: Evaluation, Analysis, Parameterization, and Applications, pp.930-945, 1994.

C. Prieur, Iterative construction of replicated designs based on Sobol' sequences, Comptes Rendus Mathematique, vol.355, issue.1, pp.10-14, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01349444

K. Kishen, On latin and hyper-Graeco-Latin cubes and hyper cubes, Current Science, vol.11, issue.3, pp.98-99, 1942.

C. R. Rao, Hypercubes of strength d leading to confounded designs in 435 factorial experiments, Bull. Calcutta Math. Soc, vol.38, issue.3, pp.67-78, 1946.

R. C. Bose and K. A. Bush, Orthogonal arrays of strength two and three, The Annals of, Mathematical Statistics, pp.508-524, 1952.

L. Gilquin, C. Prieur, and E. Arnaud, Replication procedure for grouped Sobol' indices estimation in dependent uncertainty spaces, Information and Infer- 440 ence: A, Journal of the IMA, vol.4, issue.4, pp.354-379, 2015.

B. Efron and R. Tibshirani, An introduction to the bootstrap, p.445
DOI : 10.1007/978-1-4899-4541-9

B. Efron, Nonparametric standard errors and confidence intervals, Canadian Journal of Statistics, vol.9, issue.2, pp.139-158, 1981.
DOI : 10.1137/1.9781611970593

B. Efron and R. Tibshirani, Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy, Statistical Science, vol.1, issue.1, pp.450-54, 1986.
DOI : 10.1214/ss/1177013815

T. Ishigami and T. Homma, An importance quantification technique in uncertainty analysis for computer models, [1990] Proceedings. First International Symposium on Uncertainty Modeling and Analysis, pp.398-403, 1990.
DOI : 10.1109/ISUMA.1990.151285

]. P. Bratley, B. L. Fox, and H. Niederreiter, Implementation and tests of lowdiscrepancy sequences, ACM Trans. Model. Comput. Simul, vol.2, issue.3, pp.455-195, 1992.
DOI : 10.1145/146382.146385

A. Forrester and A. Keane, Engineering design via surrogate modelling: a practical guide Additive regression and other nonparametric models, The Annals of Statistics, vol.13, issue.2, pp.460-689, 1985.
DOI : 10.1002/9780470770801

T. Hastie, gam: Generalized Additive Models, r package version 1, pp.14-18, 2017.

. .. Tu-?-t1 and . Du, We estimate S u " S with the replication procedure and formulas (5), (6) and (7) given in Section 2.2