Le lissage par fonctions splines en statistique, revue bibliographique
Statistique et analyse des données, Estimation fonctionnelle, Tome 14 (1989) no. 1, pp. 55-84. 
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Besse, Philippe; Thomas-Agnan, Christine. Le lissage par fonctions splines en statistique, revue bibliographique. Statistique et analyse des données, Estimation fonctionnelle, Tome 14 (1989) no. 1, pp. 55-84. http://www.numdam.org/item/SAD_1989__14_1_55_0/

Agarwal G. et Studden W.J., 1980. Asymptotic integrated mean square error using least squares and bias minimizing splines, Annals of Statistics , vol.8, n°6, 1307-1325. | MR | Zbl

Allen D.M., 1971. The prediction sum of squares as a criterion for selecting variables, Technical Report n °23, Dpt of Statistics, University of Kentucky.

Anselone P.M., Laurent P.J., 1968. A general method for the construction of interpolating or smoothing spline functions, Numerische Mathematik, 12, 66-82. | MR | Zbl

Ansley C.F., Kohn R., 1985. Estimation, filtering, and smoothing in state space models with incompletely specified initial conditions, Annals of Statistics, vol. 13, n°4, 1286-1316. | MR | Zbl

Atteia M., 1965. Fonctions-splines généralisées, Compte Rendu Académie des Sciences, Paris, 261, 2149-2152. | MR | Zbl

Atteia M., 1965. Généralisation de la définition et des propriétés des "splines-fonctions", Compte Rendu Académie des Sciences, Paris, 260, 3550-3553. | MR | Zbl

Atteia M., 1968. Fonctions "splines" définies sur un ensemble convexe, Numerische Mathematik, 12, 192-210. | MR | Zbl

Berlinet A., 1979. Sur les méthodes splines en estimation de la densité, Compte Rendu Académie des Sciences, Paris, 288, A, 847-850. | MR | Zbl

Berlinet A., 1980. Espaces autoreproduisants et mesure empirique, méthodes splines en estimation fonctionnelle, thèse de spécialité, Lille.

Berlinet A., 1981. Convergence des estimateurs splines de la densité, Publication de l'Institut de Statistique de l'Université de Paris, vol. 23, n°2, 1-16. | MR | Zbl

Besse P., Ramsay J., 1986. Principal components analysis of sampled functions, Psychometrika, 51, 2, 285-311. | MR | Zbl

Besse P., Vidal C., 1982. Analyse des correspondances et codage par une probabilité de transition, Statistique et Analyse des Données, vol. 7, n°3, 1-25. | Numdam | MR | Zbl

Besse P., 1989. Optimal metric in principal components analysis of longitudinal data, Data analysis and Informatics V, (Ed. E.Diday et al.), North Holland, Amsterdam. | MR

Bosq D., Lecoutre J.P., 1987. Théorie de l'estimation fonctionnelle, Economica, Paris.

Biritxinaga E., 1987. Estimation spline de la moyenne d'une fonction aléatoire, thèse de spécialité, Pau.

Breiman L., Friedman J.H., 1985. Estimating optimal transformations for multiple régression and correlation, Journal of the American Statistical Association, 80, 580-619. | MR | Zbl

Cogburn R. et Davis H.T., 1974. Periodic splines and spectral density estimation, Annals of Statistics , vol.2, 1108-1126. | MR | Zbl

Collomb G., 1981. Estimation non-paramétrique de la régression: revue bibliographique, International Statististical Review, 49, 75-93. | MR | Zbl

Collomb G., 1985. Nonparametric regression: an up-to-date bibliography, Statistics, 16, 309-324. | MR | Zbl

Cox D.D., 1983. Asymptotics for M-type smoothing splines, Annals of Statistics, vol.11, n°2, 530-551. | MR | Zbl

Cox D.D., 1984. Multivariate smoothing spline functions, SIAM Journal on Numerical Analysis, vol. 21, n°4, 789-813. | MR | Zbl

Cox D.D., Koh E., Wahba G., Yandell B.S., 1988. Testing the (parametric) null model hypothesis in (semiparametric) partial and generalized spline models, Annals of Statistics, vol.16, n°l, 113-119. | MR | Zbl

Craven P., Wahba G., 1979. Smoothing noisy data with spline functions, Numerische Mathematik , 31, 377-403. | MR | Zbl

De Boor C., 1978. A practical guide to splines, Applied Mathematical. Science 27, Springer Verlag, New-York. | MR | Zbl

Delabroye M., 1980. Comparaison entre la méthode de l'histogramme et la méthode des fonctions splines cubiques, thèse de spécialité, Rouen.

De Leeuw J., Van Rijckevorsel J.L.A., 1988. Beyond homogeneity analysis, in Component and Correspondence Analysis, ed. van Rijckevorsel J., De Leeuw J., Wiley, London. | MR

De Montricher G.F., Tapia R.A., Thompson J.R., 1975. Nonparametric maximum likelihood estimation of probability densities by penalty function methods, Annals of Statistics, vol. 3, 1329-1348. | MR | Zbl

Demmler A., Reinsch C., 1975. Oscillation matrices with spline smoothing, Numerische Mathematik , 24, 375-382. | MR | Zbl

Deny J., Lions J.L., 1954. Les espaces du type de Beppo-Levi, Annales de l'Institut Fourier, Grenoble, vol.5, 305-370. | Numdam | MR | Zbl

Dubrule O., 1983. Two methods with different objectives: splines and kriging, Journal of the International Association for Mathematical Geology, 15, 245-257.

Duchon J., 1976. Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces , R.A.I.R.0. Analyse Numérique , vol.10, n°12, 5-12 | Numdam | MR

Friedman J.H., Grosse E., Stuetzle W., 1983. Multidimensional additive spline approximation, SIAM Journal on Scientific and Statistical Computing, 4, 291-301. | MR | Zbl

Girard D., 1987. Un algorithme simple et rapide pour la validation croisée généralisée sur des problèmes de grande taille, Rapport de Recherche 669-M, IMAG, Grenoble.

Girard D., 1988 Détection de discontinuités dans un signal (ou une image) par inf-convolution spline et validation croisée : un algorithme rapide non paramétré, Rapport de Recherche 702-J-M, IMAG, Grenoble.

Golub G.H., Heath M., Wahba G., 1979. Generalized cross-validation as a method for choosing a good ridge parameter, Technometrics, vol. 21, n°2, 215-223. | MR | Zbl

Härdie W., 1989. Applied nonparametric regression, à paraître.

Huber P., 1979. Robust smoothing, in Robustness in Statistics, ed. Launer et Wilkinson, Academic, New-York. | MR

Hutchinson M.F., Hoog F.R., 1985. Smoothing noisy data whith spline functions, Numerische Mathematik, 41, 99-106. | Zbl

Kimeldorf G., Wahba G., 1970a. Spline fonctions and stochastic processes, Sankhya Series A, 32, 173-180. | Zbl

Kimeldorf G., Wahba G., 1970b. A correspondence between bayesian estimation on stochastic processes and smoothing by splines, Annals of Mathematical Statistics , vol.41, n°2, 495-502. | MR | Zbl

Kimeldorf G., Wahba G., 1971. Some results on tchebyeheffian spline functions, Journal of Mathematical Analysis and Applications , 33, 82-95. | MR | Zbl

Kohn R., Ansley C.F., 1983. On the smoothness properties of the best linear unbiased estimate of a stochastic process observed with noise, Annals of Statistics, vol. 11, n°3, 1011-1017. | MR | Zbl

Kohn R., Ansley C.F., 1987. A new algorithm for spline smoothing based on smoothing a stochastic process, SIAM Journal on Scientific and Statistical Computing, vol. 8, n°l, 33-48. | MR | Zbl

Laurent P.J., 1972. Approximation et optimisation, Hermann, Paris. | MR | Zbl

Li K.C., 1986. Asymptotic optimality of CL and generalized cross-validation in ridge regression with application to spline smoothing, Annals of Statistics, vol. 14, n°3, 1101-1112. | MR | Zbl

Lii K.S., 1978. A global measure of a spline density estimate, Annals of Statistics, vol. 6,1138-1148. | MR | Zbl

Mallows C.L., 1973. Some comments on Cp, Technometrics, vol. 15, n°4, 661-675. | Zbl

Matheron G., 1973. The intrinsic random functions and their applications, Advances in Applied Probability, 5, 439-468. | MR | Zbl

Matheron G., 1981. Splines and kriging : their formal equivalence, Syracuse University Geology Contribution 8, D.F. Merriam ed, Dept. Geology, Syracuse Univ., New-York.

Meinguet J., 1979. Multivariate interpolation at arbitrary points made simple, Journal of Applied Mathematics and Physics (ZAMP) 30, 292-304. | MR | Zbl

Messer K., 1987. A Comparison of a spline estimate to its equivalent kernel estimate, pré-publication. | Zbl

Nashed M.Z., Wahba G., 1974. Generalized inverses in reproducing kernel spaces : an approach to regularization of linear operator equations, SIAM Journal on Mathematical Analysis, vol 5, n° 6, 974-987. | MR | Zbl

Nussbaum M., 1985. Spline smoothing in regression models and asymptotic efficiency in L2, Annals of Statistics, vol. 13, n°3, 984-997. | MR | Zbl

Paihua L., 1978. Quelques méthodes numériques pour le calcul des fonctions splines à une et plusieurs variables, Thèse, Grenoble.

Poirier D.J., 1973. Piecewise regression using cubic splines, Journal of the American Statistical Association, 68, 515-524. | MR

Prakasa Rao B.L., 1983. Nonparametric fonctionnal estimation, Academic Press, New-York. | Zbl

Reinsch C. , 1967. Smoothing by spline functions, Numerische Mathematik, 10,177-183. | MR | Zbl

Reinsch C., 1971. Smoothing by spline functions II, Numerische Mathematik , 16,451-454. | MR | Zbl

Rice J., Rosenblatt M., 1983. Smoothing by splines : regression, derivatives, and deconvolution, Annals of Mathematical Statistics, vol. 11, n°1, 141-156. | MR | Zbl

Salkaukas K., 1982. Some relationships between surface splines and kriging, Multivariate Approximation Theory II, International Series of Numerical Mathematics 61, Birkhäuser. | MR | Zbl

Schoenberg J., 1964. Spline functions and the problem of graduation, Proc. Nat. Acad. Sci. U.S.A. 52, 947-950. | MR | Zbl

Schumaker L., 1981. Spline functions : basic theory, Wiley, New-York. | MR | Zbl

Schumaker L.L., Utreras F., 1988. Asymptotic properties of complete smoothing splines and applications, SIAM Journal on Scientific and Statistical Computing, vol. 9, n°l, 24-38. | MR | Zbl

Silverman B.W., 1984a. Spline smoothing : the equivalent variable kernel method, Annals of Statistics , vol.12, n°3, 898-916. | MR | Zbl

Silverman B.W., 1984b. A fast and efficient cross-validation method for smoothing parameter choice in spline regression, Journal of the American Statistical Association, vol. 79, n°387, 584-589. | MR

Silverman B.W., 1985. Some aspects of the spline smoothing approach to nonparametric regression curve fitting , Journal of the Royal Statistical Society, B, vol.47, n°l, 1-52. | MR | Zbl

Smith P., 1979. Splines as a useful statistical tool, American Statistician, 33, 57-62.

Speckman P., 1984. The asymptotic integrated mean square error for smoothing noisy data by Splines , manuscrit non publié.

Speckman P., 1985. Spline smoothing and optimal rates of convergence in non parametric regression models, Annals of Statistics , vol. 13, n°3, 970-983. | MR | Zbl

Stone M., 1974. Cross-validatory choice and assessment of statistical predictions, Journal of the Royal Statististical Society, B, vol. 36, n°2, 111-147. | MR | Zbl

Stone C.J., 1985. Additive regression and other nonparametric models, Annals of Statistics, vol. 13, 689-705. | MR | Zbl

Thomas-Agnan C. , 1988a. A family of splines for nonparametric regression and their relationships with kriging, pré-publication. | Zbl

Thomas-Agnan C. , 1988b. Smoothing periodic curves by a method of regularization, pré-publication. | Zbl

Utreras F., 1980. Sur le choix du paramètre d'ajustement dans le lissage par fonctions splines, Numerische Mathematik, 34, 15-28. | MR | Zbl

Utreras F., 1981a. On Computing robust splines and applications, SIAM Journal on Scientific and Statistical Computing, vol. 2, n°2, 153-163. | MR | Zbl

Utreras F., 1981b. Optimal smoothing of noisy data using spline functions, SIAM Journal on Scientific and Statistical Computing, vol 3, n°2, 349-362. | MR | Zbl

Utreras F., 1983. Natural spline functions, their associated eigenvalue problem, Numerische Mathematik , 42, 107-117 | MR | Zbl

Utreras F., 1987. On generalized cross-validation for multivariate smoothing spline functions, SIAM Journal on Scientific and Statistical Computing, vol. 8, n°4, 630-643. | MR | Zbl

Van Rooij P.L.J., Schurer F., 1974. A bibliography on spline functions, in Tagung über Spline Funktionen, ed. Böhmer et al., Bibliographisches Institut, Mannheim, 315-415. | MR | Zbl

Van Rijckevorsel J.L.A., 1987. The application of horseshoes and fuzzy coding in multiple correspondence analysis, DSWO press, Leiden.

Van Rijckevorsel J.L.A., 1988. Fuzzy coding and B-splines, in Component and Correspondence Analysis, ed. van Rijckevorsel J., De Leeuw J., Wiley, London. | MR

Wahba G., 1975. Smoothing noisy data with spline functions, Numerische Math., 24, 383-393. | MR | Zbl

Wahba G., 1977. Practical approximate solutions to linear operator equations when data are noisy, SIAM Journal on Numerical Analysis, vol. 14, n°4, 651-667. | MR | Zbl

Wahba G., 1978. Improper priors, spline smoothing and a problem of guarding against models errors in regression, Journal of the Royal Statististical Society, B, 3, 364-372. | MR | Zbl

Wahba G., 1981. Data-based optimal smoothing of orthogonal series density estimates, Annals of Statistics, vol. 9, n°l, 146-156. | MR | Zbl

Wahba G., 1985. A comparison of GCV and GML for choosing the smoothing parameter in the generalized spline smoothing problem, Annals of Statistics, vol.. 13, n°4, 1378-1402. | MR | Zbl

Wahba G., 1986. Partial and interaction spline models for the semiparametric estimation of functions of several variables, Proceedings of the 18th Symposium on the Interface, Colorado, March 1986, ed T.J. Boardman, Colorado State University. | MR | Zbl

Wahba G., Wold S., 1975a. A completely automatic french curve: fitting spline functions by cross-validation, Communications in Statistics, vol. 4, n°l, 1-17. | MR | Zbl

Wahba G., Wold S., 1975b. Periodic splines for spectral density estimation : the use of cross validation for determining the degree of smoothing, Communications in Statistics , vol.4, n°2, 125-141 | MR | Zbl

Watson G.S., 1983. Smoothing and interpolation by kriging and with splines, Technical Report, 241, Series 2, dept Stat, Princeton University. | MR

Wecker W.E., Ansley C.F., 1983. The signal extraction approach to nonlinear regression and spline smoothing, Journal of the American Statistical Association,vol. 78, n°381, 81-89. | MR | Zbl

Wegman E.J., Wright I.W., 1983. Splines in Statistics, Journal of the American Statistical Association, vol.78, n°382, 351-365. | MR | Zbl

Wendelberger J.G., 1987. Multiple minima of the generalized cross-validation function: paint attribute data, General Motors Research Laboratories Publications, GMR 5767.

Whittaker E.T., 1923. On a new method of graduation, Proc. Edinburgh Math. Soc., 41, 63-75.

Winsberg S., Ramsay J.O., 1980. Monotonic transformations to additivity using splines, Biometrika, 67, 3, 669-674. | MR | Zbl

Winsberg S., Ramsay J.O., 1983. Monotone spline transformations for dimension reduction, Psychometrika, 48, 575-595.

Wold S., 1974. Spline functions in data analysis, Technometrics, 16, 1-11. | MR | Zbl

Wright I.W., Wegman E.J., 1980. Isotonic, convex and related splines, Annals of Statistics, vol. 8, n°5, 1023-1035. | MR | Zbl