R. Ababou, A. C. Bagtzoglou, and E. F. Wood, On the condition number of covariance matrices in kriging, estimation, and simulation of random fields, Mathematical Geology, vol.25, issue.10, pp.99-133, 1994.
DOI : 10.1007/BF02065878

P. Abrahamsen, A review of gaussian random fields and correlation functions, 1997.

M. Abt, Approximating the mean squared prediction error in linear models under the family of exponential correlations, Statistica Sinica, vol.8, pp.511-526, 1998.

M. Abt, Estimating the Prediction Mean Squared Error in Gaussian Stochastic Processes with Exponential Correlation Structure, Scandinavian Journal of Statistics, vol.26, issue.4, pp.563-578, 1999.
DOI : 10.1111/1467-9469.00168

M. Abt and W. J. Welch, Fisher information and maximum-likelihood estimation of covariance parameters in Gaussian stochastic processes, Canadian Journal of Statistics, vol.44, issue.1, pp.127-137, 1998.
DOI : 10.2307/3315678

R. A. Adams, Sobolev Spaces, 1975.

J. R. Aldrich, R.A. Fisher and the making of maximum likelihood 1912-1922, Statistical Science, vol.12, issue.3, pp.162-176, 1997.
DOI : 10.1214/ss/1030037906

U. Amato, A. Antoniadis, and M. Pensky, Wavelet kernel penalized estimation for non-equispaced design regression, Statistics and Computing, vol.23, issue.1, pp.37-55, 2006.
DOI : 10.1007/s11222-006-5283-4
URL : https://hal.archives-ouvertes.fr/hal-00103268

W. An and Y. Sun, An Equivalence between SILF-SVR and Ordinary Kriging, Neural Processing Letters, vol.15, issue.2, pp.133-141, 2006.
DOI : 10.1007/s11063-005-4015-7

A. Antoniadis, Wavelets in statistics : a review (with discussion), Journal of the Italian Statistical Society, vol.103, 1997.
DOI : 10.1007/978-1-4612-2544-7

A. Antoniadis, Wavelet methods in statistics: some recent developments and their applications, Statistics Surveys, vol.1, issue.0, pp.16-55, 2007.
DOI : 10.1214/07-SS014
URL : https://hal.archives-ouvertes.fr/hal-00853883

G. Arfken, Mathematical Methods for Physicists, chapter Lagrange Multipliers, pp.945-950, 1985.

F. Aurenhammer and R. Klein, Voronoi diagrams, Handbook of Computational Geometry, pp.201-290, 2000.

S. Banerjee and A. E. Gelfand, On smoothness properties of spatial processes, Journal of Multivariate Analysis, vol.84, issue.1, pp.85-100, 2003.
DOI : 10.1016/S0047-259X(02)00016-7

R. A. Bates and L. Pronzato, Emulator-based global optimisation using lattices and Delaunay tesselation, Proceedings of the Third International Symposium on Sensitivity Analysis of Model Output, pp.189-192, 2001.

J. Beirlant, E. J. Dudewicz, L. Györfi, and E. C. Van-der-meulen, Nonparametric entropy estimation : an overview, International Journal of Mathematical and Statistical Sciences, vol.6, issue.1, pp.17-39, 1997.

K. Benhenni and S. Cambanis, Sampling designs for estimating integrals of stochastic processes. The Annals of Statistics, pp.161-194, 1992.

A. J. Booker, J. E. Dennis-jr, P. D. Frank, D. B. Serafini, V. Torczon et al., A rigorous framework for optimization of expensive functions by surrogates. Structural optimization, pp.1-13, 1999.

J. Bretagnolle, Formule de Chernoff pour les lois empiriques de variables à valeurs dans des espaces généraux, Astérisque, vol.68, pp.33-52, 1979.

M. Broniatowski, Estimation of the Kullback-Leibler divergence, Mathematical Methods of Statistics, vol.12, issue.4, pp.391-409, 2003.

J. N. Cawse, Experimental Design for Combinatorial and High Throughput Materials Development, 2003.

H. Chen, D. G. Simpson, and Z. Ying, Infill asymptotics for a stochastic process model with measurement error, Statistica Sinica, vol.10, pp.141-156, 2007.

J. Chilès and P. Delfiner, Geostatistics : Modeling Spatial Uncertainty, 1999.
DOI : 10.1002/9781118136188

J. H. Conway and N. J. Sloane, Sphere Packings, Lattices and Groups, 1999.

D. D. Cox and S. John, A statistical method for global optimization, [Proceedings] 1992 IEEE International Conference on Systems, Man, and Cybernetics, pp.1241-1246, 1992.
DOI : 10.1109/ICSMC.1992.271617

D. D. Cox and S. John, SDO : a statistical method for global optimization, Multidisciplinary Design Optimization : State of the Art, pp.315-329, 1995.

H. Cramer and M. R. Leadbetter, Stationary and Related Stochastic Processes, 1967.

N. A. Cressie, Statistics for Spatial Data, Revised Edition., Biometrics, vol.50, issue.1, 1993.
DOI : 10.2307/2533238

N. A. Cressie and J. Kornak, Spatial Statistics in the Presence of Location Error with an Application to Remote Sensing of the Environment, Statistical Science, vol.18, issue.4, pp.436-456, 2003.
DOI : 10.1214/ss/1081443228

N. A. Cressie and S. N. Lahiri, The Asymptotic Distribution of REML Estimators, Journal of Multivariate Analysis, vol.45, issue.2, pp.217-233, 1993.
DOI : 10.1006/jmva.1993.1034

N. A. Cressie and D. L. Zimmerman, On the stability of the geostatistical method, Mathematical Geology, vol.76, issue.1, pp.45-59, 1992.
DOI : 10.1007/BF00890087

F. Cucker and S. Smale, Best Choices for Regularization Parameters in Learning Theory: On the Bias???Variance Problem, Foundations of Computational Mathematics, vol.2, issue.4, pp.413-428, 2002.
DOI : 10.1007/s102080010030

P. Cucker and S. Smale, On the mathematical foundations of learning, Bulletin of the American Mathematical Society, vol.39, issue.01, pp.1-49, 2001.
DOI : 10.1090/S0273-0979-01-00923-5

J. A. Cuesta and C. Matran, Notes on the Wasserstein metric in Hilbert spaces. The Annals of Probability, pp.1264-1276, 1989.

I. Daubechies and B. Han, The Canonical Dual Frame of a Wavelet Frame, Applied and Computational Harmonic Analysis, vol.12, issue.3, pp.269-285, 2002.
DOI : 10.1006/acha.2002.0381

P. Deheuvels, Strong Limiting Bounds for Maximal Uniform Spacings, The Annals of Probability, vol.10, issue.4, pp.1058-1065, 1982.
DOI : 10.1214/aop/1176993728

D. Den-hertog, J. P. Kleijnen, and A. Y. Siem, The correct kriging variance estimated by bootstrapping, 2004.

L. Devroye and G. Lugosi, Combinatorial Methods in Density Estimation, 2001.
DOI : 10.1007/978-1-4613-0125-7

A. Dimnaku, R. Kincaid, and M. W. Trosset, Approximate Solutions of Continuous Dispersion Problems, Annals of Operations Research, vol.88, issue.1, pp.65-80, 2005.
DOI : 10.1007/s10479-005-2039-z

N. R. Draper and D. K. Lin, Response surface designs, Handbook of Statistics, pp.343-375, 1996.
DOI : 10.1002/0471667196.ess2268
URL : http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA147202&Location=U2&doc=GetTRDoc.pdf

W. M. Duckworth, Some binary maximin distance designs, Journal of Statistical Planning and Inference, vol.88, issue.1, pp.149-170, 2000.
DOI : 10.1016/S0378-3758(99)00183-4

B. Efron and R. J. Tibshirani, An Introduction to the Bootstrap, Collection Monographs on Statistics and Applied Probability Boca Raton (Calif, 1998.
DOI : 10.1007/978-1-4899-4541-9

J. Fan and I. Gijbels, Local Polynomial Modelling and its Applications, 1996.
DOI : 10.1007/978-1-4899-3150-4

K. Fang, R. Li, and A. Sudjianto, Design and Modeling for Computer Experiments, 2005.
DOI : 10.1201/9781420034899

I. Fazekas and A. G. Kukush, Kriging and measurement error, Probability and Statistics, vol.25, pp.139-159, 2005.

A. I. Forrester, A. J. Keane, and N. W. Bressloff, Design and Analysis of "Noisy" Computer Experiments, AIAA Journal, vol.44, issue.10, pp.2331-2339, 2006.
DOI : 10.2514/1.20068

S. Fortune, Voronoi diagrams and Delaunay triangulations, Computing in Euclidean Geometry, 1992.

S. Galanti and A. Jung, Low-Discrepancy Sequences, The Journal of Derivatives, vol.5, issue.1, pp.63-83, 1997.
DOI : 10.3905/jod.1997.407985

J. B. Gao, S. R. Gunn, C. J. Harris, and M. Brown, A probabilistic framework for SVM regression and error bar estimation, Machine Learning, pp.1-371, 2002.

S. Geman, E. Bienenstock, and R. Doursat, Neural Networks and the Bias/Variance Dilemma, Neural Computation, vol.36, issue.1, pp.1-58, 1992.
DOI : 10.1162/neco.1990.2.1.1

M. N. Gibbs, Bayesian Gaussian Processes for Regression and Classification, 1997.

I. I. Gikhman and A. V. Skorokhod, Introduction to the theory of random processes, 1996.

G. H. Golub and C. F. Van-loan, Matrix computations. Johns Hopkins Studies in the Mathematical Sciences, 1996.

Y. Gratton, Le krigeage : la méthode optimale d'interpolation spatiale. Les articles de l'Institut d'Analyse Géographique, 2002.

G. R. Grimmett and D. R. Stirzaker, Probability and Random Processes, 1992.

V. Guigue, A. Rakotomamonjy, and S. Canu, Estimation de signaux par noyau d'ondelettes, 20 e colloque sur le traitement du signal et des images, pp.449-460, 2006.

X. Guyon, Statistique et économétrie, 2001.

J. Hadamard, Sur les problèmes aux derivées partielles et leur signification physique, Princeton University Bulletin, pp.49-52, 1902.

P. Hall and S. Morton, On the estimation of entropy, Annals of the Institute of Statistical Mathematics, vol.38, issue.1, pp.69-88, 1993.
DOI : 10.1007/BF00773669

M. S. Handcock and M. L. Stein, A Bayesian Analysis of Kriging, Technometrics, vol.21, issue.3, pp.403-410, 1993.
DOI : 10.1080/00401706.1993.10485354

R. H. Hardin and N. J. Sloane, A new approach to the construction of optimal designs, Journal of Statistical Planning and Inference, vol.37, issue.3, pp.339-369, 1993.
DOI : 10.1016/0378-3758(93)90112-J

D. A. Harville, Bayesian inference for variance components using only error contrasts, Biometrika, vol.61, issue.2, pp.383-385, 1974.
DOI : 10.1093/biomet/61.2.383

D. A. Harville and D. R. Jeske, Mean Squared Error of Estimation or Prediction under a General Linear Model, Journal of the American Statistical Association, vol.2, issue.419, pp.724-731, 1992.
DOI : 10.1007/BF00048668

T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning : Data Mining, Inference, and Prediction, 2001.

M. E. Havrda and F. Charvát, Quantification method of classification processes : concept of structural ?-entropy, Kybernetika, vol.3, pp.30-35, 1967.

A. S. Hedayat, N. J. Sloane, and J. Stufken, Orthogonal Arrays : Theory and Applications, 1999.
DOI : 10.1007/978-1-4612-1478-6

J. A. Hoeting, R. A. Davis, A. A. Merton, and S. E. Thompson, Model Selection For Geostatistical Models, Ecological Applications, vol.16, issue.1, pp.87-98, 2006.
DOI : 10.1080/03610927808827599

B. Hofmann, Regularization for Applied Inverse and Ill-Posed Problems, J. Teubner, 1986.

K. M. Irvine, A. I. Gitelman, and J. A. Hoeting, Spatial designs and properties of spatial correlation: Effects on covariance estimation, Journal of Agricultural, Biological, and Environmental Statistics, vol.33, issue.4, pp.450-469, 2007.
DOI : 10.1198/108571107X249799

S. Jaffard, Y. Meyer, and R. D. Ryan, Wavelets : Tools for Science & Technology, Society for Industrial and Applied Mathematics (SIAM), 2001.
DOI : 10.1137/1.9780898718119

R. Jin, W. Chen, and A. Sudjianto, An efficient algorithm for constructing optimal design of computer experiments, Journal of Statistical Planning and Inference, vol.134, issue.1, pp.268-287, 2005.
DOI : 10.1016/j.jspi.2004.02.014

P. W. John, M. E. Johnson, L. M. Moore, and D. Ylvisaker, Minimax distance designs in two-level factorial experiments, Journal of Statistical Planning and Inference, vol.44, issue.2, pp.249-263, 1995.
DOI : 10.1016/0378-3758(94)00047-Y

M. E. Johnson, L. M. Moore, and D. Ylvisaker, Minimax and maximin distance designs, Journal of Statistical Planning and Inference, vol.26, issue.2, pp.131-148, 1990.
DOI : 10.1016/0378-3758(90)90122-B

D. R. Jones, A taxonomy of global optimization methods based on response surfaces, Journal of Global Optimization, vol.21, issue.4, pp.345-383, 2001.
DOI : 10.1023/A:1012771025575

D. R. Jones, M. Schonlau, and W. J. Welch, Efficient global optimization of expensive black-box functions, Journal of Global Optimization, vol.13, issue.4, pp.455-492, 1998.
DOI : 10.1023/A:1008306431147

R. N. Kackar and D. A. Harville, Approximations for standard errors of estimators of fixed and random effects in mixed linear models, Journal of the American Statistical Association, issue.388, pp.79853-862, 1984.

M. G. Kendall and A. Stuart, The advanced theory of statistics, 1973.

J. T. Kent and K. V. Mardia, The link between kriging and thin-plate splines. Probability, Statistics and Optimisation : a Tribute to Peter Whittle, pp.325-339, 1994.

A. Keziou, Utilisation des divergences entre mesures en statistique inférentielle, 2003.

A. I. Khuri and J. A. Cornell, Response Surfaces : Designs and Analyses, 1996.

G. Kimeldorf and G. Wahba, Some results on Tchebycheffian spline functions, Journal of Mathematical Analysis and Applications, vol.33, issue.1, pp.82-95, 1971.
DOI : 10.1016/0022-247X(71)90184-3

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Optimization by Simulated Annealing, Science, vol.220, issue.4598, pp.671-680, 1983.
DOI : 10.1126/science.220.4598.671

T. G. Kolda, R. M. Lewis, and V. J. Torczon, Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods, SIAM Review, vol.45, issue.3, pp.385-482, 2003.
DOI : 10.1137/S003614450242889

L. Kozachenko and N. Leonenko, On statistical estimation of entropy of a random vector, Problems of Information Transmission, vol.23, issue.2, pp.95-101, 1987.

M. F. Kratz, Level crossings and other level functionals of stationary Gaussian processes, Probability Surveys, vol.3, issue.0, pp.230-288, 2006.
DOI : 10.1214/154957806000000087
URL : https://hal.archives-ouvertes.fr/hal-00174410

F. Y. Kuo and I. H. Sloan, Lifting the curse of dimensionality, Notices of the AMS, vol.52, issue.11, pp.1320-1329, 2005.

S. N. Lahiri, On inconsistency of estimators based on spatial data under infill asymptotics, Sankhya : The Indian Journal of Statistics, vol.58, pp.403-417, 1996.

R. L. Lam, W. J. Welch, and S. S. Young, Uniform Coverage Designs for Molecule Selection, Technometrics, vol.44, issue.2, pp.99-109, 2002.
DOI : 10.1198/004017002317375055

B. Laurent, Adaptive estimation of a quadratic functional of a density by model selection, ESAIM: Probability and Statistics, vol.9, pp.1-18, 2005.
DOI : 10.1051/ps:2005001

N. Leonenko, L. Pronzato, and V. Savani, A class of Rényi information estimators for multidimensional densities. The Annals of Statistics, pp.2153-2182, 2008.

R. Li and A. Sudjianto, Analysis of Computer Experiments Using Penalized Likelihood in Gaussian Kriging Models, Technometrics, vol.47, issue.2, pp.111-120, 2005.
DOI : 10.1198/004017004000000671

W. Light and H. Wayne, On Power Functions and Error Estimates for Radial Basis Function Interpolation, Journal of Approximation Theory, vol.92, issue.2, pp.245-266, 1998.
DOI : 10.1006/jath.1997.3118

R. Linder, Les plans d'expériences. Un outil indispensable à l'expérimentateur, 2005.

G. Lindgren, Lectures on Stationary Stochastic Processes ; a Course for PhD students in Mathematical Statistics and other fields, 1999.

W. L. Loh, Fixed-domain asymptotics for a subclass of Matérn-type gaussian random fields. The Annals of Statistics, pp.2344-2394, 2005.

W. L. Loh and T. K. Lam, Estimating structured correlation matrices in smooth gaussian random field models. The Annals of Statistics, pp.880-904, 2000.

S. N. Lophaven, H. B. Nielsen, and J. Sondergaard, Aspects of the matlab toolbox DACE, 2002.

S. N. Lophaven, H. B. Nielsen, and J. Sondergaard, DACE, a matlab kriging toolbox, 2002.

L. Luh, The embedding theory of native spaces. Approximation Theory & Its Applications, pp.90-104, 2001.

L. Luh, The equivalence theory of native spaces. Approximation Theory & Its Applications, pp.76-96, 2001.

L. Luh, On Wu and Schaback's error bound. arXiv :math/0602087v1, 2006.

M. N. Luki? and J. H. Beder, Stochastic processes with sample paths in reproducing kernel Hilbert spaces. Transactions of the, pp.3945-3969, 2001.

D. J. Mackay, Introduction to Gaussian processes, Neural Networks and Machine Learning, NATO ASI, pp.133-166, 1998.

W. R. Madych and S. A. Nelson, Multivariate interpolation and conditionally positive definite functions. Approximation Theory and its Applications, pp.77-89, 1988.
DOI : 10.1090/s0025-5718-1990-0993931-7

W. R. Madych and S. A. Nelson, Multivariate interpolation and conditionally positive definite functions. II, Mathematics of Computation, vol.54, issue.189, pp.211-230, 1990.
DOI : 10.1090/S0025-5718-1990-0993931-7

K. V. Mardia, Maximum likelihood estimation for spatial models, Spatial Statistics : Past, Present and Future, pp.203-253, 1990.

K. V. Mardia and R. J. Marshall, Maximum likelihood estimation of models for residual covariance in spatial regression, Biometrika, vol.71, issue.1, pp.135-146, 1984.
DOI : 10.1093/biomet/71.1.135

K. V. Mardia and A. J. Watkins, On multimodality of the likelihood in the spatial linear model, Biometrika, vol.76, issue.2, pp.289-295, 1989.
DOI : 10.1093/biomet/76.2.289

J. Martin and T. Simpson, A Monte Carlo Simulation of the Kriging Model, 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 2004.
DOI : 10.2514/6.2004-4483

T. J. Mitchell and M. D. Morris, Bayesian design and analysis of computer experiments : Two examples, Statistica Sinica, vol.2, pp.359-379, 1992.

J. Mockus, V. Tiesis, and A. Zilinskas, The application of bayesian methods for seeking the extremum, Towards Global Optimisation, vol.2, pp.117-129, 1978.

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

W. G. Müller, Collecting Spatial Data. Optimum Design of Experiments for Random Fields, 2003.

I. J. Myung, Tutorial on maximum likelihood estimation, Journal of Mathematical Psychology, vol.47, issue.1, pp.90-100, 2003.
DOI : 10.1016/S0022-2496(02)00028-7

C. J. Paciorek and M. Schervish, Spatial modelling using a new class of nonstationary covariance functions, Environmetrics, vol.99, issue.5, pp.483-506
DOI : 10.1002/env.785

G. Pagès and J. Printems, Optimal quadratic quantization for numerics: the Gaussian case, Monte Carlo Methods and Applications, pp.135-165, 2003.
DOI : 10.1515/156939603322663321

E. Pardo-igúzquiza, MLREML: A computer program for the inference of spatial covariance parameters by maximum likelihood and restricted maximum likelihood, Computers & Geosciences, vol.23, issue.2, pp.153-162, 1997.
DOI : 10.1016/S0098-3004(97)85438-6

R. Penrose, A generalized inverse for matrices, Proceedings of the Cambridge Philosophical Society, pp.406-413, 1955.
DOI : 10.1093/qmath/2.1.189

W. R. Pestman, Mathematical Statistics : an Introduction, 1998.

T. Poggio and S. Smale, The mathematics of learning : Dealing with data. Notices of the, pp.537-544, 2003.

M. J. Powell, On the use of quadratic models in unconstrained minimization without derivatives, Optimization Methods and Software, vol.19, issue.3-4, 2003.
DOI : 10.1007/s10107-003-0430-6

L. Pronzato, One-step ahead adaptative D-optimal design on a finite design space is asymptotically optimal. Metrika

L. Pronzato and E. Thierry, Sequential experimental design and response optimisation, Statistical Methods & Applications, vol.41, issue.6, pp.277-292, 2002.
DOI : 10.1007/BF02509828
URL : https://hal.archives-ouvertes.fr/hal-01002348

L. Pronzato and E. Thierry, Robust design with nonparametric models : Prediction of second-order characteristics of process variability by kriging, 13th IFAC Symposium on System Identification, pp.560-565

F. Pukelsheim, Optimal design of experiments, SIAM, 2006.
DOI : 10.1137/1.9780898719109

A. Rakotomamonjy and S. Canu, Frames, reproducing kernels, regularization and learning, The Journal of Machine Learning Research, vol.6, pp.1485-1515, 2005.

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

G. K. Robinson, That BLUP is a Good Thing: The Estimation of Random Effects, Statistical Science, vol.6, issue.1, pp.15-51, 1991.
DOI : 10.1214/ss/1177011926

L. Rüschendorf, Wasserstein metric, Encyclopaedia of Mathematics, 2001.

H. Rue and L. Held, Gaussian Markov Random Fields : Theory and Applications, 2005.
DOI : 10.1201/9780203492024

J. Sacks and S. Schiller, Spatial Designs, Statistical Decision Theory and Related Topics IV, pp.385-395, 1988.
DOI : 10.1007/978-1-4612-3818-8_32

J. Sacks, S. B. Schiller, and W. J. Welch, Designs for Computer Experiments, Technometrics, vol.15, issue.18, pp.41-47, 1989.
DOI : 10.1080/00401706.1989.10488474

J. Sacks, W. J. Welch, T. J. Mitchell, and H. P. Wynn, Design and Analysis of Computer Experiments, Statistical Science, vol.4, issue.4, pp.409-435, 1989.
DOI : 10.1214/ss/1177012413

T. R. Sahama and N. T. Diamond, Sample size considerations and augmentation of computer experiments, Journal of Statistical Computation and Simulation, vol.68, issue.4, pp.307-319, 2001.
DOI : 10.2307/1269548

T. J. Santner, B. I. Williams, and W. I. Notz, The Design and Analysis of Computer Experiments, 2003.
DOI : 10.1007/978-1-4757-3799-8

M. J. Sasena, P. Y. Papalambros, and P. Goovaerts, Metamodeling sampling criteria in a global optimization framework, 8th Symposium on Multidisciplinary Analysis and Optimization, pp.189-192, 2000.
DOI : 10.2514/6.2000-4921

R. Schaback, Native Hilbert spaces for radial basis functions I New developments in approximation theory, International Series of Numerical Mathematics, pp.255-282, 1998.

R. Schaback, A unified theory of radial basis functions, Numerical analysis in the 20th century, pp.165-177, 2000.
DOI : 10.1016/S0377-0427(00)00345-9

C. Scheidt, Analyse statistique d'expériences simulées : modélisation adaptative de réponses non régulières par krigeage et plans d'expériences, Application à la quantification des incertitudes en ingénierie des réservoirs pétroliers, 2006.

B. Schölkopf, R. Herbrich, A. J. Smola, and R. Williamson, A Generalized Representer Theorem, ESPRIT Working Group in Neural and Computational Learning II, 2000.
DOI : 10.1007/3-540-44581-1_27

M. Schonlau and W. J. Welch, Global optimization with nonparametric function fitting, Proceedings of the Section on Physical and Engineering Sciences, pp.183-186, 1996.

M. Schonlau, W. J. Welch, and D. Jones, A data-analytic approach to bayesian global optimization, American Statistical Association Proceedings, Section of Physical Engineering Sciences, pp.186-191, 1997.

M. Schonlau, W. J. Welch, and D. R. Jones, Global versus local search in constrained optimization of computer models, New Developments and Applications in Experimental Design, pp.11-25, 1998.
DOI : 10.1214/lnms/1215456182

C. E. Shannon, A mathematical theory of communication. The Bell System Technical Journal, pp.379-423, 1948.

M. C. Shewry and H. P. Wynn, Maximum entropy sampling, Journal of Applied Statistics, vol.14, issue.2, pp.165-170, 1987.
DOI : 10.2307/2987990

J. S. Simonoff, Smoothing Methods in Statistics, 1996.
DOI : 10.1007/978-1-4612-4026-6

A. J. Smola, T. T. Friess, and B. Schölkopf, General cost functions for support vector regression, Advances in Neural Information Processing Systems, pp.585-591, 1999.

A. J. Smola and B. Schölkopf, A tutorial on support vector regression, Statistics and Computing, vol.14, issue.3, pp.199-222, 2004.
DOI : 10.1023/B:STCO.0000035301.49549.88

A. J. Smola, B. Schölkopf, and K. Müller, The connection between regularization operators and support vector kernels, Neural Networks, vol.11, issue.4, pp.637-649, 1998.
DOI : 10.1016/S0893-6080(98)00032-X

A. J. Smola, B. Schölkopf, and K. Müller, General cost functions for support vector regression, Proceedings of the Ninth Australian Conference on Neural Networks, pp.79-83, 1998.

M. Stehlík, Some properties of exchange design algorithms under correlation, Research Report Series / Department of Statistics and Mathematics, vol.28, 2006.

M. L. Stein, Interpolation of Spatial Data : Some Theory for Kriging, 1999.
DOI : 10.1007/978-1-4612-1494-6

M. L. Stein, Predicting random fields with increasing dense observations, The Annals of Applied Probability, vol.9, issue.1, pp.242-273, 1999.
DOI : 10.1214/aoap/1029962604

M. L. Stein, The screening effect in kriging. The Annals of Statistics, pp.298-323, 2002.

M. L. Stein, Equivalence of Gaussian measures for some nonstationary random fields, Journal of Statistical Planning and Inference, vol.123, issue.1, pp.1-11, 2004.
DOI : 10.1016/S0378-3758(03)00144-7

M. L. Stein, Nonstationary spatial covariance functions, 2005.

M. L. Stein, Z. Chi, and L. J. Welty, Approximating likelihoods for large spatial data sets, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.17, issue.2, pp.275-296, 2004.
DOI : 10.1016/0167-9473(91)90055-7

A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems, 1977.

E. Tillier, Développement d'un algorithme d'optimisation pour la synthèse de catalyseurs à haut débit, 2004.

V. J. Torczon, On the Convergence of Pattern Search Algorithms, SIAM Journal on Optimization, vol.7, issue.1, pp.1-25, 1997.
DOI : 10.1137/S1052623493250780

M. W. Trosset, Approximate maximin distance designs, Proceedings of the Section on Physical and Engineering Sciences, pp.223-227, 1999.

C. Tsallis, Possible generalization of Boltzmann-Gibbs statistics, Journal of Statistical Physics, vol.8, issue.1-2, pp.479-487, 1988.
DOI : 10.1007/BF01016429

E. R. Van-dam, Two-dimensional minimax latin hypercube designs, 2005.

E. R. Van-dam, B. Husslage, D. Hertog, and H. Melissen, Maximin Latin Hypercube Designs in Two Dimensions, Operations Research, vol.55, issue.1, pp.158-169, 2007.
DOI : 10.1287/opre.1060.0317

A. W. Van and . Vaart, Maximum likelihood estimation of parameters under a spatial sampling scheme. The Annals of Statistics, pp.2049-2057, 1996.

A. W. Van and . Vaart, Asymptotic Statistics. Cambridge series in statistical and probabilistic mathematics, 1998.

V. Vapnik, Statistical Learning Theory, 1998.

V. Vapnik, The Nature of Statistical Learning Theory. Statistics for Engineering and Information Science, 2000.

E. Vazquez, Modélisation comportementale de systèmes non-linéaires multivariables par méthodes à noyaux et applications, 2005.

E. Vazquez and J. Bect, On the convergence of the expected improvement algorithm, 2008.

J. Villemonteix, E. Vasquez, and E. Walter, An informational approach to the global optimization of expensive-to-evaluate functions, Journal of Global Optimization, vol.10, issue.5
DOI : 10.1007/s10898-008-9354-2
URL : https://hal.archives-ouvertes.fr/hal-00354262

G. Wahba, Spline Models for Observational Data, CBMS?NSF Regional Conference Series in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), vol.59, 1992.
DOI : 10.1137/1.9781611970128

G. Wahba, Support Vector Machines, Reproducing Kernel Hilbert Spaces and the randomized GACV, 1998.

M. Waldman, H. Li, and M. Hassan, Novel algorithms for the optimization of molecular diversity of combinatorial libraries, Journal of Molecular Graphics and Modelling, vol.18, issue.4-5, pp.412-426, 2000.
DOI : 10.1016/S1093-3263(00)80095-9

M. P. Wand and M. C. Jones, Kernel Smoothing, 1995.
DOI : 10.1007/978-1-4899-4493-1

A. G. Watson and R. J. Barnes, Infill sampling criteria to locate extremes, Mathematical Geology, vol.15, issue.no. 3, pp.589-608, 1995.
DOI : 10.1007/BF02093902

C. Wei, Bayesian Approach to Support Vector Machines, 2003.

H. Wendland, Scattered Data Approximation, Cambridge Monographs on Applied and Computational Mathematics, 2005.
DOI : 10.1017/CBO9780511617539

C. K. Williams, Regression with Gaussian Processes, Proceedings of the first international conference on Mathematics of neural network : models, algorithms and applications, pp.378-382, 1997.
DOI : 10.1007/978-1-4615-6099-9_66
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.26.1026

C. K. Williams and C. E. Rasmussen, Regression with Gaussian Processes, Advances in Neural Information Processing Systems, pp.514-520, 1996.
DOI : 10.1007/978-1-4615-6099-9_66

Z. Wu and R. Schaback, Local error estimates for radial basis function interpolation of scattered data, IMA Journal of Numerical Analysis, vol.13, issue.1, pp.13-27, 1993.
DOI : 10.1093/imanum/13.1.13

H. P. Wynn, The Sequential Generation of $D$-Optimum Experimental Designs, The Annals of Mathematical Statistics, vol.41, issue.5, pp.1655-1664, 1970.
DOI : 10.1214/aoms/1177696809

H. P. Wynn, Maximum entropy sampling and general equivalence theory7 -advances in model-oriented design and analysis, Proceedings of the 7th international workshop, pp.211-218, 2007.

Y. Xiong, W. Chen, D. Apley, and X. Ding, A non-stationary covariance-based Kriging method for metamodelling in engineering design, International Journal for Numerical Methods in Engineering, vol.128, issue.6, pp.733-756, 2007.
DOI : 10.1002/nme.1969

Z. Ying, Asymptotic properties of a maximum likelihood estimator with data from a Gaussian process, Journal of Multivariate Analysis, vol.36, issue.2, pp.280-296, 1991.
DOI : 10.1016/0047-259X(91)90062-7

Z. Ying, Maximum likelihood estimation of parameters under a spatial sampling scheme. The Annals of Statistics, pp.1567-1590, 1993.

H. Zhang, Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics, Journal of the American Statistical Association, vol.99, issue.465, pp.250-261, 2004.
DOI : 10.1198/016214504000000241

H. Zhang and D. L. Zimmerman, Towards reconciling two asymptotic frameworks in spatial statistics, Biometrika, vol.92, issue.4, pp.921-936, 2005.
DOI : 10.1093/biomet/92.4.921

Z. Zhu and M. L. Stein, Spatial sampling design for prediction with estimated parameters, Journal of Agricultural, Biological, and Environmental Statistics, vol.33, issue.D22, pp.24-44, 2006.
DOI : 10.1198/108571106X99751

Z. Zhu and H. Zhang, Spatial sampling design under the infill asymptotic framework, Environmetrics, vol.44, issue.4, pp.323-337, 2005.
DOI : 10.1002/env.772

D. L. Zimmerman, Optimal network design for spatial prediction, covariance parameter estimation, and empirical prediction, Environmetrics, vol.2, issue.6, pp.635-652, 2006.
DOI : 10.1002/env.769

D. L. Zimmerman and N. Cressie, Mean squared prediction error in the spatial linear model with estimated covariance parameters, Annals of the Institute of Statistical Mathematics, vol.33, issue.1, pp.27-43, 1992.
DOI : 10.1007/BF00048668

D. L. Zimmerman and M. B. Zimmerman, A Comparison of Spatial Semivariogram Estimators and Corresponding Ordinary Kriging Predictors, Technometrics, vol.32, issue.1, pp.77-91, 1991.
DOI : 10.1080/00401706.1984.10487921

V. M. Zolotarev, Lévy metric, Encyclopaedia of Mathematics, 2001.

A. Zygmund, Trigonometrical series, 1955.