REGRESSION NON PARAMETRIQUE DANS UN MODELE GAUSSIEN
Mots-clés :
Estimation de la densité, estimation de la régression, estimation à noyau, bandes de confiance.Résumé
L'objet de ce travail est de construire des estimateurs de régression non paramétrique asymptotiquement optimaux, sous l'hypothèse que les lois sous-jacentes sont gaussiennes. Les résultats que nous obtenons présentent l'intérêt d'être directement applicables en analyse exploratoire des données.Téléchargements
Références
- Akaike, H. (1954). An approximation of the density function.
Ann. Inst. Statist. Math., 6, 127-132.
- Bosq, D. et Lecoutre, J. P. (1987). Théorie de l’Estimation
Fonctionnelle. Economica, Paris.
- Deheuvels, P. and Mason, D. M. (2004). General asymptotic
confidence bands based on kernel-type function estimators.
Stat. Infer. Soc. Processes, 7, 225-277.
- Devroye, L. (1978). The uniform convergence of the
Nadaraya-Watson regression function Estimate. Can. J.
Statist., 6, 179-191.
- Devroye, L. and Györfi, L. (1985). Nonparametric Density
Estimation: The L1 view. Wiley, New York.
- Devroye, L. and Lugosi, G. (2001). Combinatorial methods in
density estimation. Springer Series in Statistics. Springer-
Verlag, New York.
- Einmahl, U. and Mason, D. M. (2000). An empirical process
approach to the uniform consistency of kernel-type function
estimators. J. Theoretical Prob., 13, 1-37.
- Härdle, W. (1990). Applied Nonparametric Regression.
Cambridge University Press, Cambridge.
- Härdle, W., Jansen, P. and Serfling, R. (1988). Strong
uniform consistency rates for estimators of conditional
functionals. Ann. Statist., 16, 1428-1449.
- Izenman, A. J. (1991). Recents developments in
nonparametric density estimation. J. Amer. Statist. Assoc.,
, no. 413, 205-224.
- Nadaraya, E. A. (1964). On estimating regression. Theor.
Prob. Appl., 9, 141-142.
- Nadaraya, E. A. (1989). Nonparametric Estimation of
Probability Densities and Regression Curves. Kluwer,
Dordrecht.
- Parzen, E. (1962). On estimation of a probability density
function and mode. Ann. Math. Statist. 33, 1065-1076.
- Prakasa Rao, B. L. S. (1983). Nonparametric Functional
Estimation. Academic Press, New York.
- Rosenblatt, M. (1956). Remarks on some nonparametric
estimates of a density function. Ann. Math. Statist., 27, 832-
- Roussas, G. (1990). Nonparametric Functional Estimation
and Related Topics. NATO ASI series 355. Kluwer,
Dordrecht.
- Scott, D. W. (1992). Multivariate Density Estimation-
Theory, Practice and Visualization. Wiley, New York.
- Silverman, B. W. (1986). Density Estimation for Statistics
and Data Analysis. Chapman and Hall, London.
- Wand, M. P. and Jones, M. C. (1995). Kernel Smoothing.
Chapman and Hall, London.
- Watson, G. S. (1964). Smooth Regression Analysis.
Sankhya A, 26, 359-372.
