B. Table, Simulation study on TII estimators (Section 3.5), simulation results of test function high 2 nd order. method interaction true D i,j mean( D i,j ) sd( D i,j ) RMSE

G. E. Archer, A. Saltelli, and I. M. 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

B. Bettonvil, Factor screening by sequential bifurcation, Communications in Statistics - Simulation and Computation, vol.3, issue.1, pp.165-185, 1995.
DOI : 10.1080/03610919508813236

G. Blatman and B. Sudret, Efficient computation of global sensitivity indices using sparse polynomial chaos expansions, Reliability Engineering & System Safety, vol.95, issue.11, pp.1216-1229, 2010.
DOI : 10.1016/j.ress.2010.06.015

R. E. Caflisch, Monte Carlo and quasi-Monte Carlo methods, Acta Numerica, vol.73, pp.1-49, 1998.
DOI : 10.1137/S0036142994277468

R. Confalonieri, G. Bellocchi, S. Bregaglio, M. Donatelli, and M. Acutis, Comparison of sensitivity analysis techniques: A case study with the rice model WARM, Ecological Modelling, vol.221, issue.16, pp.1897-1906, 2010.
DOI : 10.1016/j.ecolmodel.2010.04.021

J. Cornfield and J. W. Tukey, Average Values of Mean Squares in Factorials, The Annals of Mathematical Statistics, vol.27, issue.4, pp.907-949, 1956.
DOI : 10.1214/aoms/1177728067

G. Csárdi and T. Nepusz, The igraph software package for complex network research. InterJournal, Complex Systems, 1695.

R. I. Cukier, H. B. Levine, and K. E. Shuler, Nonlinear sensitivity analysis of multiparameter model systems, Journal of Computational Physics, vol.26, issue.1, pp.1-42, 1978.
DOI : 10.1016/0021-9991(78)90097-9

C. Daniel, One-at-a-Time Plans, Journal of the American Statistical Association, vol.31, issue.3, pp.353-360, 1973.
DOI : 10.1080/01621459.1973.10482433

C. De-boor, A practical guide to splines, of Applied mathematical sciences, 2001.
DOI : 10.1007/978-1-4612-6333-3

N. Durrande, D. Ginsbourger, O. Roustant, and L. Carraro, ANOVA kernels and RKHS of zero mean functions for model-based sensitivity analysis, Journal of Multivariate Analysis, vol.115, pp.57-67, 2013.
DOI : 10.1016/j.jmva.2012.08.016
URL : https://hal.archives-ouvertes.fr/hal-00601472

B. Efron and C. Stein, The Jackknife Estimate of Variance, The Annals of Statistics, vol.9, issue.3, pp.586-596, 1981.
DOI : 10.1214/aos/1176345462

K. Fang, R. Li, and A. Sudjianto, Design and modeling for computer experiments . Computer science and data analysis series, Boca Raton, 2006.

J. Fort, T. Klein, A. Lagnoux, and B. Laurent, Estimation of the Sobol indices in a linear functional multidimensional model, Journal of Statistical Planning and Inference, vol.143, issue.9, pp.1590-1605, 2013.
DOI : 10.1016/j.jspi.2013.04.007
URL : https://hal.archives-ouvertes.fr/hal-00685998

J. Fort, T. Klein, and N. Rachdi, New sensitivity analysis subordinated to a contrast, Communications in Statistics - Theory and Methods, vol.1, issue.4, 2014.
DOI : 10.1016/S0010-4655(02)00280-1
URL : https://hal.archives-ouvertes.fr/hal-00821308

J. Franco, D. Dupuy, O. Roustant, G. Damblin, and B. Iooss, DiceDesign: Designs of Computer Experiments, 2014.

J. H. Friedman and B. E. Popescu, Predictive learning via rule ensembles, The Annals of Applied Statistics, vol.2, issue.3, pp.916-954, 2008.
DOI : 10.1214/07-AOAS148

J. Fruth and M. Jastrow, seqSAFI: sequential sensitivity analysis for functional inputs. R package version 1.0, available on http, 2014.

J. Fruth, O. Roustant, and S. Kuhnt, Sequential designs for sensitivity analysis of functional inputs in computer experiments, Reliability Engineering & System Safety, vol.134, 2014.
DOI : 10.1016/j.ress.2014.07.018
URL : https://hal.archives-ouvertes.fr/hal-00943509

J. Fruth, O. Roustant, and S. Kuhnt, Total interaction index: A variance-based sensitivity index for second-order interaction screening, Journal of Statistical Planning and Inference, vol.147, pp.212-223, 2014.
DOI : 10.1016/j.jspi.2013.11.007
URL : https://hal.archives-ouvertes.fr/hal-00631066

J. Fruth, O. Roustant, and T. Mühlenstädt, The fanovagraph package: Visualization of interaction structures and construction of block-additive Kriging models, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00795229

F. Gamboa, A. Janon, T. Klein, and A. Lagnoux, Sensitivity indices for multivariate outputs, Comptes Rendus Mathematique, vol.351, issue.7-8, pp.7-8, 2013.
DOI : 10.1016/j.crma.2013.04.016
URL : https://hal.archives-ouvertes.fr/hal-00800847

O. Garcia-cabrejo and A. Valocchi, Global Sensitivity Analysis for multivariate output using Polynomial Chaos Expansion, Reliability Engineering & System Safety, vol.126, pp.25-36, 2014.
DOI : 10.1016/j.ress.2014.01.005

W. 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

T. Homma and A. Saltelli, Importance measures in global sensitivity analysis of nonlinear models, Reliability Engineering & System Safety, vol.52, issue.1, pp.1-17, 1996.
DOI : 10.1016/0951-8320(96)00002-6

G. Hooker, Discovering additive structure in black box functions, Proceedings of the 2004 ACM SIGKDD international conference on Knowledge discovery and data mining , KDD '04, pp.575-580, 2004.
DOI : 10.1145/1014052.1014122

B. Iooss and M. Ribatet, Global sensitivity analysis of computer models with functional inputs, Reliability Engineering & System Safety, vol.94, issue.7, pp.1194-1204, 2009.
DOI : 10.1016/j.ress.2008.09.010
URL : https://hal.archives-ouvertes.fr/hal-00243156

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

M. Ivanov and S. Kuhnt, A Parallel Optimization Algorithm based on FANOVA Decomposition, Quality and Reliability Engineering International, vol.3, issue.2, 2014.
DOI : 10.1002/qre.1710

G. M. James, J. Wang, and J. Zhu, Functional linear regression that???s interpretable, The Annals of Statistics, vol.37, issue.5A, pp.2083-2108, 2009.
DOI : 10.1214/08-AOS641

A. Janon, T. Klein, A. Lagnoux, M. Nodet, and C. Prieur, Asymptotic normality and efficiency of two Sobol index estimators, ESAIM: Probability and Statistics, vol.18, 2013.
DOI : 10.1051/ps/2013040
URL : https://hal.archives-ouvertes.fr/hal-00665048

M. J. Jansen, Analysis of variance designs for model output, Computer Physics Communications, vol.117, issue.1-2, pp.35-43, 1999.
DOI : 10.1016/S0010-4655(98)00154-4

R. W. Katz, Techniques for estimating uncertainty in climate change scenarios and impact studies, Climate Research, vol.20, issue.2, pp.167-185, 2002.
DOI : 10.3354/cr020167

J. P. Kleijnen, Sensitivity analysis and related analyses: A review of some statistical techniques, Journal of Statistical Computation and Simulation, vol.1, issue.1-4, pp.111-142, 1997.
DOI : 10.2307/1266728

D. G. Krige, A statistical approach to some basic mine valuation problems on the witwatersrand, Journal of the Chemical, Metallurgical and Mining Society of South Africa, vol.52, issue.6, pp.119-139, 1951.

S. Kucherenko, B. Delpuech, B. Iooss, and S. Tarantola, Application of the control variate technique to estimation of total sensitivity indices, Reliability Engineering & System Safety, vol.134, 2014.
DOI : 10.1016/j.ress.2014.07.008

S. Kucherenko, M. Rodriguez-fernandez, C. Pantelides, and N. Shah, Monte Carlo evaluation of derivative-based global sensitivity measures, Reliability Engineering & System Safety, vol.94, issue.7, pp.1135-1148, 2009.
DOI : 10.1016/j.ress.2008.05.006

M. Lamboni, B. Iooss, A. Popelin, and F. Gamboa, Derivative-based global sensitivity measures: General links with Sobol??? indices and numerical tests, Mathematics and Computers in Simulation, vol.87, pp.45-54, 2013.
DOI : 10.1016/j.matcom.2013.02.002
URL : https://hal.archives-ouvertes.fr/hal-00666473

M. Lamboni, H. Monod, and D. Makowski, Multivariate sensitivity analysis to measure global contribution of input factors in dynamic models, Reliability Engineering & System Safety, vol.96, issue.4, pp.450-459, 2011.
DOI : 10.1016/j.ress.2010.12.002
URL : https://hal.archives-ouvertes.fr/hal-00999840

J. S. Lehman, T. J. Santner, and I. N. William, Designing computer experiments to determinate robust control variables, Statistica Sinica, vol.14, pp.571-590, 2004.

L. Lilburne and S. Tarantola, Sensitivity analysis of spatial models, International Journal of Geographical Information Science, vol.58, issue.2, pp.151-168, 2009.
DOI : 10.1016/j.ress.2005.11.048

R. Liu and A. B. Owen, Estimating Mean Dimensionality of Analysis of Variance Decompositions, Journal of the American Statistical Association, vol.101, issue.474, pp.712-721, 2006.
DOI : 10.1198/016214505000001410

T. A. Mara, Extension of the RBD-FAST method to the computation of global sensitivity indices, Reliability Engineering & System Safety, vol.94, issue.8, pp.1274-1281, 2009.
DOI : 10.1016/j.ress.2009.01.012
URL : https://hal.archives-ouvertes.fr/hal-01093036

A. Marrel, B. Iooss, B. Laurent, and O. Roustant, Calculations of Sobol indices for the Gaussian process metamodel, Reliability Engineering & System Safety, vol.94, issue.3, pp.742-751, 2009.
DOI : 10.1016/j.ress.2008.07.008
URL : https://hal.archives-ouvertes.fr/hal-00239494

W. Mauntz, Global sensitivity analysis of general nonlinear systems, 2002.

M. D. Mckay, Evaluating prediction uncertainty, Div. of Systems Technol- ogy, 1995.
DOI : 10.2172/29432

H. Monod, C. Naud, and D. Makowski, Uncertainty and sensitivity analysis for crop models, Working with dynamic crop models, pp.55-99, 2006.

M. D. Morris, Factorial Sampling Plans for Preliminary Computational Experiments, Technometrics, vol.1, issue.2, pp.161-174, 1991.
DOI : 10.2307/1266468

M. D. Morris, An overview of group factor screening Screening methods for experimentation in industry, drug discovery, and genetics, pp.191-206, 2006.

M. D. Morris, Gaussian Surrogates for Computer Models With Time-Varying Inputs and Outputs, Technometrics, vol.128, issue.1, pp.42-50, 2012.
DOI : 10.1080/02664768700000020

M. D. Morris and T. J. Mitchell, Exploratory designs for computational experiments, Journal of Statistical Planning and Inference, vol.43, issue.3, pp.381-402, 1995.
DOI : 10.1016/0378-3758(94)00035-T

T. Mühlenstädt, J. Fruth, and O. Roustant, Computer experiments with functional inputs and scalar outputs by a norm-based approach, Statistics and Computing, vol.55, issue.3, 2014.
DOI : 10.1007/s11222-016-9672-z

T. Mühlenstädt, O. Roustant, L. Carraro, and S. Kuhnt, Data-driven Kriging models based on FANOVA-decomposition, Statistics and Computing, vol.34, issue.4, pp.723-738, 2012.
DOI : 10.1007/s11222-011-9259-7

A. B. Owen, Better estimation of small sobol' sensitivity indices, ACM Transactions on Modeling and Computer Simulation, vol.23, issue.2, pp.1-17, 2013.
DOI : 10.1145/2457459.2457460

A. B. Owen, Variance Components and Generalized Sobol' Indices, SIAM/ASA Journal on Uncertainty Quantification, vol.1, issue.1, pp.19-41, 2013.
DOI : 10.1137/120876782
URL : http://arxiv.org/abs/1205.1774

E. Plischke, An effective algorithm for computing global sensitivity indices (EASI), Reliability Engineering & System Safety, vol.95, issue.4, pp.354-360, 2010.
DOI : 10.1016/j.ress.2009.11.005

G. Pujol, B. Iooss, A. J. With, L. L. From-laurent-gilquin, P. Gratiet et al., sensitivity: Sensitivity Analysis. R package version 1, pp.8-10, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00936929

V. Punzo and B. Ciuffo, Sensitivity analysis of car-following models: methodology and application, Proc. 90th Annual TRB Meeting, 2011.

R. Team, R: A Language and Environment for Statistical Computing, 2014.

H. Rabitz, O. F. Alis, J. Shorter, and K. Shim, Efficient input???output model representations, Computer Physics Communications, vol.117, issue.1-2, pp.11-20, 1999.
DOI : 10.1016/S0010-4655(98)00152-0

J. O. Ramsay and B. W. Silverman, Functional Data Analysis. Springer Series in Statistics, Biometrical Journal, vol.40, issue.1, 1997.
DOI : 10.1002/(SICI)1521-4036(199804)40:1<56::AID-BIMJ56>3.0.CO;2-#

C. E. Rasmussen and C. K. Williams, Gaussian Processes in Machine Learning, 2006.
DOI : 10.1162/089976602317250933

O. Roustant, J. Fruth, B. Iooss, and S. Kuhnt, Crossed-derivative based sensitivity measures for interaction screening, Mathematics and Computers in Simulation, vol.105, pp.105-118, 2014.
DOI : 10.1016/j.matcom.2014.05.005
URL : https://hal.archives-ouvertes.fr/hal-00845446

O. Roustant, D. Ginsbourger, and Y. Deville, Packages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization, Journal of Statistical Software, vol.51, issue.1, pp.1-55, 2012.
DOI : 10.18637/jss.v051.i01
URL : https://hal.archives-ouvertes.fr/hal-00495766

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. Saltelli and R. Bolado, An alternative way to compute Fourier amplitude sensitivity test (FAST), Computational Statistics & Data Analysis, vol.26, issue.4, pp.445-460, 1998.
DOI : 10.1016/S0167-9473(97)00043-1

A. Saltelli, K. Chan, and E. M. Scott, Sensitivity analysis. Wiley series in probability and statistics, 2000.
URL : https://hal.archives-ouvertes.fr/inria-00386559

A. Saltelli, M. Ratto, S. Tarantola, and F. Campolongo, Sensitivity analysis practices: Strategies for model-based inference, Reliability Engineering & System Safety, vol.91, issue.10-11, pp.1109-1125, 2006.
DOI : 10.1016/j.ress.2005.11.014

A. Saltelli, S. Tarantola, and K. P. Chan, A Quantitative Model-Independent Method for Global Sensitivity Analysis of Model Output, Technometrics, vol.60, issue.1, pp.39-56, 1999.
DOI : 10.1007/BF01166355

T. J. Santner, B. J. Williams, and W. I. Notz, The design and analysis of computer experiments. Springer series in statistics, 2003.

J. H. Schaibly and K. E. Shuler, Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. II Applications, The Journal of Chemical Physics, vol.59, issue.8, pp.3879-3888, 1973.
DOI : 10.1063/1.1680572

I. M. Sobol-', Sensitivity estimates for non linear mathematical models, Mathematical Modelling and Computational Experiments, vol.1, pp.407-414, 1993.

I. M. Sobol-', Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates, Mathematics and Computers in Simulation, vol.55, pp.1-3, 2001.

I. M. Sobol-' and A. Gershman, On an alternative global sensitivity estimator, Samo 95: Theory and Applications of Sensitivity Analysis of Model Output in Computer Simulation, pp.40-42, 1995.

I. M. Sobol-' and S. Kucherenko, Derivative based global sensitivity measures and their link with global sensitivity indices, Mathematics and Computers in Simulation, vol.79, issue.10, pp.3009-3017, 2009.
DOI : 10.1016/j.matcom.2009.01.023

S. Tarantola, D. Gatelli, and T. A. Mara, Random balance designs for the estimation of first order global sensitivity indices, Reliability Engineering & System Safety, vol.91, issue.6, pp.717-727, 2006.
DOI : 10.1016/j.ress.2005.06.003
URL : https://hal.archives-ouvertes.fr/hal-01065897

J. Tissot and C. Prieur, Bias correction for the estimation of sensitivity indices based on random balance designs, Reliability Engineering & System Safety, vol.107, pp.205-213, 2012.
DOI : 10.1016/j.ress.2012.06.010
URL : https://hal.archives-ouvertes.fr/hal-00507526

H. Ul-hassan, J. Fruth, A. Güner, and A. E. Tekkaya, Finite element simulations for sheet metal forming process with functional input for the minimization of springback, IDDRG conference 2013, pp.393-398, 2013.

A. W. Van-der-vaart, Asymptotic statistics, 1998.
DOI : 10.1017/CBO9780511802256

J. S. Walker, A primer on wavelets and their scientific applications, 1999.
DOI : 10.1201/9781420050011

G. S. Watson, A Study of the Group Screening Method, Technometrics, vol.38, issue.3, pp.371-388, 1961.
DOI : 10.1080/00401706.1961.10489954