@. X. Bay, L. Grammont, H. Maatoukhal, @. X. Bay, L. Grammont et al., Une structure par terme est une courbe qui d'´ ecrit l'´ evolution d'une A New Method for Smoothing and Interpolating with Inequality Constraints. Submitted, preprint http Generalization of the Kimeldorf- Wahba Correspondence in the Case of Constrained Interpolation Kriging of Financial Term-Structures. Submitted, preprint https, Article%20Yeild%20Curve_modif_Hassan_25_Sep.pdf B.2 Chapitre proceeding dans une conférence sélective ? H. Maatouk and X. Bay (2014). A New Rejection Sampling Method for Truncated Multivariate Gaussian Random Variables Restricted to Convex Sets. To appear in Monte Carlo and Quasi-Monte Carlo Methods 2014, p.2016, 2015.

. Ku-leuven, United Kingdom ? Mascot-Num annual conference 2014 Zürich, Switzerland ? Eleventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing http://isfa.univ-lyon1.fr/le_seminaire_du_laboratoire_ saf.html ? Gaussian Random Field Simulation GRF-Sim2014 Workshop, Liste des conférences internationales ? Spatial Statistics Emerging Patterns Belgium C.1 Invitations ? Séminairè a ISFA (Institut de ScienceFinancì ere et d'Assurances) ? Journée des thèses avec l'IRSN (Institut de Radioprotection et de Sûreté Nucléaire), 2013.

. Bibliographieabrahamsen, P. Benth-]-abrahamsen, and F. E. Benth, Kriging with inequality constraints, Mathematical Geology, vol.33, issue.6, pp.719-744, 2001.

H. Akima, A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures, Journal of the ACM, vol.17, issue.4, pp.589-602, 1970.
DOI : 10.1145/321607.321609

F. Ametrano and M. Bianchetti, Bootstrapping the illiquidity : Multiple yield curves construction for market coherent forward rates estimation, 2009.

L. Andersen, Discount curve construction with tension splines, Review of Derivatives Research, vol.9, issue.3, pp.227-267, 2007.
DOI : 10.1007/s11147-008-9021-2

E. Andersson, L. Andersson, and T. Elfving, Interpolation and approximation by monotone cubic splines, Journal of Approximation Theory, vol.66, issue.3, pp.302-333, 1991.
DOI : 10.1016/0021-9045(91)90033-7

P. Anger, B. Anger, and C. Portenier, Radon Integrals : An Abstract Approach to Integration and Riesz Representation Through Function Cones, Progress in Mathematics, 1992.
DOI : 10.1007/978-1-4612-0377-3

N. Aronszajn, Theory of reproducing kernels. Transactions of the, p.68, 1950.

F. Bachoc, Cross Validation and Maximum Likelihood estimations of hyper-parameters of Gaussian processes with model misspecification, Computational Statistics & Data Analysis, vol.66, issue.0, pp.6655-69, 2013.
DOI : 10.1016/j.csda.2013.03.016

T. Berlinet, A. Berlinet, and C. Thomas-agnan, Reproducing Kernel Hilbert Spaces in Probability and Statistics, 2004.
DOI : 10.1007/978-1-4419-9096-9

C. Botts, An accept-reject algorithm for the positive multivariate normal distribution, Computational Statistics, vol.5, issue.4, pp.1749-1773, 2013.
DOI : 10.1007/s00180-012-0377-2

V. Boyd, S. Boyd, and L. Vandenberghe, Convex Optimization, 2004.

J. Breslaw, Random sampling from a truncated multivariate normal distribution, Applied Mathematics Letters, vol.7, issue.1, pp.1-6, 1994.
DOI : 10.1016/0893-9659(94)90042-6

G. Casella, G. Casella, and E. I. George, Explaining the Gibbs sampler. The American Statistician, pp.167-174, 1992.

. Chibane, Building Curves on a Good Basis, SSRN Electronic Journal, 2009.
DOI : 10.2139/ssrn.1394267

N. Chopin, Fast simulation of truncated Gaussian distributions, Statistics and Computing, vol.82, issue.398, pp.275-288, 2011.
DOI : 10.1007/s11222-009-9168-1

. Cramér, . Leadbetter, H. Cramér, and R. Leadbetter, Stationary and related stochastic processes : sample function properties and their applications. Wiley series in probability and mathematical statistics. Tracts on probability and statistics, 1967.

N. A. Cressie, Statistics for Spatial Data, 1993.

. Csiszar, Mem pixel correlated solutions for generalized moment and interpolation problems. Information Theory, IEEE Transactions on, issue.7, pp.452253-2270, 1999.

[. Veiga, . Marrel, S. Da-veiga, and A. Marrel, Gaussian process modeling with inequality constraints, Annales de la faculté des sciences de Toulouse, pp.529-555, 2012.
DOI : 10.5802/afst.1344

. Delecroix, Functional estimation under shape constraints, Journal of Nonparametric Statistics, vol.6, issue.1, pp.69-89, 1996.
DOI : 10.1080/10485259608832664

T. Delecroix, M. Delecroix, and C. Thomas-agnan, A shape constrained smoother : simulation study, Computational Statistics, vol.10, pp.155-175, 1995.

L. Devroye, Non-Uniform Random Variate Generation, 1986.
DOI : 10.1007/978-1-4613-8643-8

D. Dole, Cosmo : A constrained scatterplot smoother for estimating convex, monotonic transformations, Journal of Business & Economic Statistics, vol.17, issue.4, pp.444-455, 1999.

A. Dontchev, Best Interpolation in a Strip, Journal of Approximation Theory, vol.73, issue.3, pp.334-342, 1993.
DOI : 10.1006/jath.1993.1045

J. L. Doob, Stochastic process measurability conditions. Annales de l'institut Fourier, pp.3-4163, 1975.

B. Dougherty, Nonnegativity-, monotonicity-, or convexity-preserving cubic and quintic Hermite interpolation, Mathematics of Computation, vol.52, issue.186, pp.52471-494, 1989.
DOI : 10.1090/S0025-5718-1989-0962209-1

K. Dubrule, O. Dubrule, and C. Kostov, An interpolation method taking into account inequality constraints: I. Methodology, Mathematical Geology, vol.16, issue.6, pp.33-51, 1986.
DOI : 10.1007/BF00897654

J. Duchon, Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces, Revue fran??aise d'automatique, informatique, recherche op??rationnelle. Analyse num??rique, vol.10, issue.R3, pp.5-12, 1976.
DOI : 10.1051/m2an/197610R300051

M. Ellis, N. Ellis, and R. Maitra, Multivariate Gaussian Simulation Outside Arbitrary Ellipsoids, Journal of Computational and Graphical Statistics, vol.16, issue.3, pp.692-708, 2007.
DOI : 10.1198/106186007X238431

. Emery, Simulating Large Gaussian Random Vectors Subject to Inequality Constraints by Gibbs Sampling, Mathematical Geosciences, vol.22, issue.4, pp.1-19, 2013.
DOI : 10.1007/s11004-013-9495-9

. Freulon, X. Fouquet-]-freulon, and C. Fouquet, Conditioning a Gaussian model with inequalities, Geostatistics Tróia '92, pp.201-212, 1993.
DOI : 10.1007/978-94-011-1739-5_17

C. P. Fries, Curves and term structure models : Definition, calibration and application of rate curves and term structure models, 2013.

C. Fritsch, F. Fritsch, and R. Carlson, Monotone Piecewise Cubic Interpolation, SIAM Journal on Numerical Analysis, vol.17, issue.2, pp.238-246, 1980.
DOI : 10.1137/0717021

G. Gamboa, F. Gamboa, and E. Gassiat, Bayesian methods and maximum entropy for ill-posed inverse problems, The Annals of Statistics, vol.25, issue.1, pp.328-350, 1997.
DOI : 10.1214/aos/1034276632

. Gander, . Wanner, M. J. Gander, and G. Wanner, From Euler, Ritz, and Galerkin to Modern Computing, SIAM Review, vol.54, issue.4, pp.627-666, 2012.
DOI : 10.1137/100804036

. Gelfand, Bayesian Analysis of Constrained Parameter and Truncated Data Problems Using Gibbs Sampling, Journal of the American Statistical Association, vol.47, issue.418, pp.523-532, 1992.
DOI : 10.1093/biomet/60.2.319

J. Geweke, Exact inference in the inequality constrained normal linear regression model, Journal of Applied Econometrics, vol.59, issue.2, pp.127-141, 1986.
DOI : 10.1002/jae.3950010203

J. Geweke, Efficient Simulation from the Multivariate Normal and Student-t Distributions Subject to Linear Constraints and the Evaluation of Constraint Probabilities, Computing Science and Statistics : Proceedings of the 23rd Symposium on the Interface, pp.571-578, 1991.

H. Maatouk, B. Gilks, . Wild, W. R. Gilks, and P. Wild, Adaptive Rejection Sampling for Gibbs Sampling, Journal of the Royal Statistical Society. Series C (Applied Statistics ), issue.2, pp.41337-348, 1992.

. Golchi, Monotone Emulation of Computer Experiments, SIAM/ASA Journal on Uncertainty Quantification, vol.3, issue.1, pp.370-392, 2015.
DOI : 10.1137/140976741

. Goldfarb, . Idnani, D. Goldfarb, and A. Idnani, A numerically stable dual method for solving strictly convex quadratic programs, Mathematical Programming, vol.27, issue.1, pp.1-33, 1983.
DOI : 10.1007/BF02591962

W. E. Griffiths, A Gibbs sampler for the parameters of a truncated multivariate normal distribution. Department of Economics -Working Papers Series 856, 2002.

. Gupta, A multivariate skew normal distribution, Journal of Multivariate Analysis, vol.89, issue.1, pp.181-190, 2004.
DOI : 10.1016/S0047-259X(03)00131-3

W. Hagan, P. S. Hagan, and G. West, Interpolation Methods for Curve Construction, Applied Mathematical Finance, vol.15, issue.1, pp.89-129, 2006.
DOI : 10.1080/13504860500396032

. Hörmann, Automatic Nonuniform Random Variate Generation, Statistics and Computing, 2004.

J. M. Hyman, Accurate Monotonicity Preserving Cubic Interpolation, SIAM Journal on Scientific and Statistical Computing, vol.4, issue.4, pp.645-654, 1983.
DOI : 10.1137/0904045

Y. Iwashita, Piecewise polynomial interpolations, 2013.

S. Janson, Gaussian Hilbert Spaces, Cambridge Tracts in Mathematics, vol.129, 1997.
DOI : 10.1017/CBO9780511526169

Y. Wu and G. T. , Efficient Algorithms for Generating Truncated Multivariate Normal Distributions, Acta Mathematicae Applicatae Sinica, English Series, vol.27, issue.4, p.601, 2011.

S. Kenyon, C. Kenyon, and R. Stamm, Discounting, Libor, CVA and Funding : Interest Rate and Credit Pricing, 2012.
DOI : 10.1057/9781137268525

. Kimeldorf, . Wahba, G. S. Kimeldorf, and G. Wahba, A Correspondence Between Bayesian Estimation on Stochastic Processes and Smoothing by Splines, The Annals of Mathematical Statistics, vol.41, issue.2, pp.495-502, 1971.
DOI : 10.1214/aoms/1177697089

. Kostov, . Dubrule, C. Kostov, and O. Dubrule, An interpolation method taking into account inequality constraints: II. Practical approach, Mathematical Geology, vol.48, issue.1, pp.53-73, 1986.
DOI : 10.1007/BF00897655

B. Kotecha, . Djuric, J. H. Kotecha, and P. Djuric, Gibbs sampling approach for generation of truncated multivariate Gaussian random variables, 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258), pp.1757-1760, 1999.
DOI : 10.1109/ICASSP.1999.756335

. Laud, Sampling Some Truncated Distributions Via Rejection Algorithms, Communications in Statistics - Simulation and Computation, vol.40, issue.6, pp.391111-1121, 2010.
DOI : 10.2307/1266749

P. J. Laurent, Approximation et optimisation. Enseignement des sciences, 1972.

P. J. Laurent, An algorithm for the computation of spline functions with inequality constraints, 1980.

F. Le-floc-'h, Stable interpolation for the yield curve, 2013.

. Li, . Ghosh, Y. Li, and S. K. Ghosh, Efficient sampling method for truncated multivariate normal and Student t-distribution subject to linear inequality constraints

P. Loridan, Sur la minimisation de fonctionnelles convexes par pénalisation. Revue Française d'informatique et de recherche opérationnelle, série rouge tome 5, pp.117-133, 1971.

B. Maatouk, H. Maatouk, and X. Bay, Gaussian Process Emulators for Computer Experiments with Inequality Constraints. in revision, p.1096751
URL : https://hal.archives-ouvertes.fr/hal-01096751

B. Maatouk, H. Maatouk, and X. Bay, A New Rejection Sampling Method for Truncated Multivariate Gaussian Random Variables Restricted to Convex Sets. To appear in Monte Carlo and Quasi-Monte Carlo Methods 2014, 2014.
URL : https://hal.archives-ouvertes.fr/emse-01339361

D. Marcotte, D. Marcotte, and M. David, Trend surface analysis as a special case of IRF-k kriging, Mathematical Geology, vol.5, issue.7, pp.821-824, 1988.
DOI : 10.1007/BF00890194

M. Martino, L. Martino, and J. Miguez, An adaptive accept/reject sampling algorithm for posterior probability distributions, 2009 IEEE/SP 15th Workshop on Statistical Signal Processing, pp.45-48, 2009.
DOI : 10.1109/SSP.2009.5278644

M. Martino, L. Martino, and J. Miguez, A novel rejection sampling scheme for posterior probability distributions, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing, pp.2921-2924, 2009.
DOI : 10.1109/ICASSP.2009.4960235

G. Matheron, C. Micchelli, and F. Utreras, Down-to-earth statistics : Solutions looking for geological problems, chapter splines and kriging : their formal equivalence. [Micchelli and Utreras Smoothing and Interpolation in a Convex Subset of a Hilbert Space, SIAM Journal on Scientific and Statistical Computing, vol.9, issue.4, pp.728-746, 1981.

H. Maatouk, B. Nair, and M. , Linear Operator Equations : Approximation and Regularization, 2009.

S. Nelson, C. R. Nelson, and A. F. Siegel, Parsimonious Modeling of Yield Curves, The Journal of Business, vol.60, issue.4, pp.473-489, 1987.
DOI : 10.1086/296409

P. , R. Philippe, A. Robert, and C. P. , Perfect simulation of positive Gaussian distributions, Statistics and Computing, vol.13, issue.2, pp.179-186, 2003.

J. O. Ramsay, Monotone Regression Splines in Action, Statistical Science, vol.3, issue.4, pp.425-441, 1988.
DOI : 10.1214/ss/1177012761

J. O. Ramsay, Estimating smooth monotone functions, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.60, issue.2, pp.365-375, 1998.
DOI : 10.1111/1467-9868.00130

. Riihimaki, J. Vehtari-]-riihimaki, and A. Vehtari, Gaussian processes with monotonicity information, AISTATS, volume 9 of JMLR Proceedings, pp.645-652, 2010.

C. P. Robert, Simulation of truncated normal variables, Statistics and Computing, vol.82, issue.2, 1995.
DOI : 10.1007/BF00143942

URL : https://hal.archives-ouvertes.fr/hal-00431310

R. , C. Robert, C. P. Casella, and G. , Monte Carlo Statistical Methods, 2004.

. Roustant, Dicekriging , diceoptim : Two r packages for the analysis of computer experiments by krigingbased metamodeling and optimization, Journal of Statistical Software, vol.51, issue.1, pp.1-55, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00495766

. Santner, The Design and Analysis of Computer Experiments, 2003.
DOI : 10.1007/978-1-4757-3799-8

L. Schwartz, Sous-espaces hilbertiens d???espaces vectoriels topologiques et noyaux associ??s (Noyaux reproduisants), Journal d'Analyse Math??matique, vol.238, issue.1, pp.115-256, 1964.
DOI : 10.1007/BF02786620

. Smith, . Wilson, . Smith, and T. Wilson, Fitting yield curves with long term constraints, 2001.

F. Utreras and M. L. Varas, Monotone Interpolation of Scattered Data in R s . Constructive Approximation, pp.49-68, 1991.

F. I. Utreras, Convergence rates for monotone cubic spline interpolation, Journal of Approximation Theory, vol.36, issue.1, pp.86-90, 1982.
DOI : 10.1016/0021-9045(82)90074-0

B. Villalobos, . Wahba, M. Villalobos, and G. Wahba, Inequality-Constrained Multivariate Smoothing Splines with Application to the Estimation of Posterior Probabilities, Journal of the American Statistical Association, vol.78, issue.397, pp.82239-248, 1987.
DOI : 10.1080/01621459.1987.10478426

J. Von-neumann-]-von-neumann, Various Techniques Used in Connection with Random Digits, J. Res. Nat. Bur. Stand, vol.12, pp.36-38, 1951.

A. Wolberg, G. Wolberg, and I. Alfy, Monotonic cubic spline interpolation, Proceedings of Computer Graphics International, pp.188-195, 1999.

I. Alfy, An energy-minimization framework for monotonic cubic spline interpolation, Journal of Computational and Applied Mathematics, vol.143, issue.2, pp.145-188, 2002.

W. Wright, I. W. Wright, and E. J. Wegman, Isotonic, Convex and Related Splines, The Annals of Statistics, vol.8, issue.5, pp.1023-1035, 1980.
DOI : 10.1214/aos/1176345140

URL : http://projecteuclid.org/download/pdf_1/euclid.aos/1176345140

W. Xiaojing, Bayesian Modeling Using Latent Structures, 2012.

P. Xuming, H. Xuming, and S. Peide, Monotone B-spline Smoothing, Journal of the American Statistical Association, vol.93, pp.643-650, 1996.