Estimateurs à noyau itérés : synthèse bibliographique

Biau, Gérard

Journal de la Société française de statistique, Tome 140 (1999) no. 1, pp. 41-67.

[1] Akaike H. (1954). An approximation to the density function. Annals of the Institute of Statistical Mathematics, 6 : 127-132. | MR | Zbl

[2] Berlinet A. et Devroye L. (1989). Estimation d'une densité : un point sur la méthode du noyau. Statistique et Analyse des Données, 14 : 1-32.

[3] Berlinet A. et Devroye L. (1994). A comparison of kernel density estimates. Publications de l'Institut de Statistique de l'Université de Paris, 38 : 3-59. | MR | Zbl

[4] Birgé L. et Massart P. (1997). From model selection to adaptative estimation. In Festschrift for LeCam, 55-87. New York : Springer-Verlag. | MR | Zbl

[5] Bosq D. et Lecoutre J.P. (1987). Théorie de l'Estimation Fonctionnelle. Paris : Economica.

[6] Bowman A.W. (1984). An alternative method of cross-validation for the smoothing of density estimates. Biometrika, 71 : 353-360. | MR

[7] Burman P. (1985). A data dependent approach to density estimation. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 69 : 609-628. | MR | Zbl

[8] Cao R., Cuevas A. et González-Manteiga W. (1994). A comparative study of several smoothing methods in density estimation. Computational Statistics and Data Analysis, 17 : 153-176. | Zbl

[9] Chiu S.T. (1991). Bandwith selection for kernel density estimation. The Annals of Statistics, 19 : 1883-1905. | MR | Zbl

[10] Chiu S.T. (1992). An automatic bandwith selector for kernel density estimation. Biometrika, 79 : 771-782. | MR | Zbl

[11] Chow Y.S., Geman S. et Wu L.D. (1983) Consistent cross-validated density estimation. The Annals of Statistics, 11 : 25-38. | MR | Zbl

[12] Deheuvels P. (1974). Conditions nécessaires et suffisantes de convergence ponctuelle presque sûre et uniforme presque sûre des estimateurs de la densité. Comptes Rendus Mathématiques de l'Académie des Sciences de Paris, 278 : 1217-1220. | MR | Zbl

[13] Deheuvels P. (1977). Estimation non paramétrique de la densité par histogrammes généralisés. Revue de Statistique Appliquée, 25 : 5-42. | MR

[14] Deheuvels P. et Hominal P. (1980) Estimation automatique de la densité. Revue de Statistique Appliquée, 28 : 25-55. | Numdam | MR | Zbl

[15] Devroye L. (1987). A Course m Density Estimation. Boston : Birkhauser. | Zbl

[16] Devroye L. (1989). A universal lower bound for the kernel estimate. Statistics and Probability Letters, 8 : 419-423. | MR | Zbl

[17] Devroye L. (1994). On good deterministic smoothing sequences for kernel density estimates. The Annals of Statistics, 22 : 886-889. | MR | Zbl

[18] Devroye L. (1997). Universal smoothing factor selection in density estimation : theory and practice. Test, 6 : 223-320. | MR | Zbl

[19] Devroye L. et Gyorfi L. (1985) Nonparametric Density Estimation the L1 View. New York : Wiley. | MR

[20] Devroye L. et Lugosi G. (1996). A universally acceptable smoothing factor for kernel density estimates. The Annals of Statistics, 24 : 2499-2512. | MR | Zbl

[21] Devroye L. et Lugosi G. (1997). Nonasymptotic universal smoothing factors, kernel complexity, and Yatracos classes. The Annals of Statistics, 25 : 2626-2637. | MR | Zbl

[22] Duin R.P.W. (1976) On the choice of smoothing parameters for Parzen estimators of probability density functions. IEEE Transactions on Computers, 25 : 1175-1179. | Zbl

[23] Engel J., Herrmann E. et Gasser T. (1994) An iterative bandwith selector for kernel estimation of densities and their derivatives. Journal of Nonparametric Statistics, 4 : 21-34. | MR

[24] Fan J. et Marron J.S. (1992). Best possible constant for bandwith selection. The Annals of Statistics, 20 : 2057-2070. | MR | Zbl

[25] Gijbels I. et Mammen E. (1998). Local adaptivity of kernel estimates with plug-in local bandwith selectors. Board of the Foundation of the Scandmavian Journal of Statistics, 25 : 503-520. | MR | Zbl

[26] Habbema J.D.F., Hermans J. et Vandenbroek K. (1974). A stepwise discriminant analysis program using density estimation. In Compstat, ed. G. Bruckmann, 101-110. Wien : Physica-Verlag. | MR

[27] Hall P. (1982). Cross-validation in density estimation. Biometrika, 69 : 383-390. | MR | Zbl

[28] Hall P. (1983). Large-sample optimality of least squares cross-validation in density estimation. The Annals of Statistics, 11 : 1156-1174. | MR | Zbl

[29] Hall P. (1985). Asymptotic theory of minimum integrated square error for multivariate density estimation. In Multwariate Analysis VI, ed. Krishnaiah, 289-309. Amsterdam . North-Holland. | MR | Zbl

[30] Hall P. (1993). On plug-in rules for local smoothing of density estimators. The Annals of Statistics, 21 : 694-710. | MR | Zbl

[31] Hall P. et Marron J.S. ( 1987a). Estimation of integrated squared density derivatives. Statistics and Probability Letters, 6 : 109-115. | MR | Zbl

[32] Hall P. et Marron J.S. ( 1987b). Extent to which least squares cross-validation minimises integrated square error in nonparametric density estimation. Probability Theory and Related Fields, 74 : 567-581. | MR | Zbl

[33] Hall P. et Marron J.S. ( 1987c). On the amount of noise inherent in bandwith selection of a kernel density estimator. The Annals of Statistics, 15 : 163-181. | MR | Zbl

[34] Hall P. et Marron J.S. ( 1991a). Local minima in cross-validation functions. Journal of the Royal Statistical Association, B53 : 245-252. | MR | Zbl

[35] Hall P. et Marron J.S. ( 1991b). Lower bounds for bandwith selection in density estimation. Probability Theory and Related Fields, 90 : 149-173. | MR | Zbl

[36] Hall P., Marron J.S. et Park B.U. (1992). Smoothed cross-validation. Probability Theory and Related Fields, 92 : 1-20. | MR | Zbl

[37] Hall P., Sheather S.J., Jones M.C. et Marron J.S. (1991). On optimal data-based bandwith selection in kernel density estimation Biometrika, 78 : 263-269. | MR | Zbl

[38] Hall P. et Wand M.P. (1988). Minimizing L1 distance in nonparametric density estimation. Journal of Multivariate Analysis, 26 : 59-88. | MR | Zbl

[39] Jones M. C., Marron J.S. et Park B.U. (1991). A simple root n bandwith selector. The Annals of Statistics, 19 : 1919-1932. | MR | Zbl

[40] Jones M.C. et Sheather S. J. (1991). Using non-stochastic terms to advantage in kernel-based estimation of integrated squared density derivatives. Statistics and Probability Letters, 11 : 511-514. | MR | Zbl

[41] Kim W.C., Park B.U. et Marron J.S. (1994). Asymptotically best bandwith selectors in kernel density estimation. Statistics and Probability Letters, 19 : 119-127. | MR | Zbl

[42] Marron J.S. (1985). An asymptotically efficient solution to the bandwith problem of kernel density estimation. The Annals of Statistics, 13 : 1011-1023. | MR | Zbl

[43] Marron J.S. (1987). A comparison of cross-validation techniques in density estimation. The Annals of Statistics, 15 : 152-162. | MR | Zbl

[44] Marron J.S. (1988). Automatic smoothing parameter selection : a survey. Empirical Economics, 13 : 187-208.

[45] Marron J.S. (1989) Comments on a data-based bandwith selector. Computational Statistics and Data Analysis, 8 : 155-170. | MR | Zbl

[46] Marron J.S. (1992). Bootstrap bandwith selection. In Exploring the Limits of Bootstrap, ed. R. le Page et L. Billard, 249-262. New York : Wiley. | MR | Zbl

[47] Nadaray E.A. (1974). On the integral mean square error of some nonparametric estimates for the density function. Theory of Probability and its Applications, 19 : 133-141. | Zbl

[48] Park B.U. (1989). On the plug-in bandwith selectors in kernel density estimation. Journal of the Korean Statistical Society, 18 : 107-117. | MR

[49] Park B.U. et Marron J.S. (1990). Comparison of data-driven bandwith selectors. Journal of the American Statistical Association, 85 : 66-72.

[50] Park B.U. et Marron J.S. (1992). On the use of pilot estimators in bandwith selection. Journal of Nonparametric Statistics, 1 : 231-240. | MR

[51] Parzen E. (1962). On the estimation of a probability density function and the mode. The Annals of Mathematical Statistics, 33 : 1065-1076. | MR | Zbl

[52] Rosenblatt M. (1956). Remarks on some nonparametric estimates of a density function. The Annals of Mathematical Statistics, 27 : 832-837. | MR | Zbl

[53] Rosenblatt M. (1971). Curve estimates. The Annals of Mathematical Statistics, 42 : 1815-1842. | MR | Zbl

[54] Rudemo M. (1982). Empirical choice of histograms and kernel density estimators. Scandinavian Journal of Statistics, 9 : 65-78. | MR | Zbl

[55] Schuster E.F. et Gregory G. G. (1981). On the nonconsistency of maximum likelihood nonparametric density estimators. In Computer Science and Statistics : Proceedings of the 13th Symposium on the Interface, ed. W.F. Eddy, 295-298. New York : Springer Verlag. | MR

[56] Scott D.W. (1985). Averaged shifted histograms : effective nonparametric density estimators in several dimensions The Annals of Statistics, 13 : 1024-1040. | MR | Zbl

[57] Scott D.W. (1992). Multivariate Density Estimation : Theory, Practice, and Visualisation. New York : Wiley. | MR | Zbl

[58] Scott D.W. et Factor L.E. (1981). Monte Carlo study of three data-based nonparametric probability density estimators. Journal of the American Statistical Association, 76 : 9-15. | Zbl

[59] Scott D.W., Tapia R.A. et Thompson J.R. (1977). Kernel density estimation revisited. Nonlinear Analysis, Theory, Methods and Applications, 1 : 339-372. | MR | Zbl

[60] Scott D.W. et Terrell G. R. (1987). Biased and unbiased cross-validation in density estimation. Journal of the American Statistical Association, 82 : 1131-1146. | MR | Zbl

[61] Sheather S.J. (1983). A data-based algorithm for choosing the window width when estimating the density at a point. Computational Statistics and Data Analysis, 1 : 229-238. | Zbl

[62] Sheather S.J. (1986). An improved data-based algorithm for choosing the window width when estimating the density at a point. Computational Statistics and Data Analysis, 4 : 61-65.

[63] Sheather S.J. et Jones M.C. (1991). A reliable data-based bandwith selection method for kernel density estimation. Journal of the Royal Statistical Society, B53 : 683-690. | MR | Zbl

[64] Silverman B.W. (1986). Density Estimation for Statistics and Data Analysis. London : Chapman and Hall. | MR | Zbl

[65] Simonoff J.S. (1996). Smoothing Methods in Statistics. New York : Springer-Verlag. | MR | Zbl

[66] Stone C.J. (1984) An asymptotically optimal window selection rule for kernel density estimates. The Annals of Statistics, 12 : 1285-1297. | MR | Zbl

[67] Terrell G.R. et Scott D.W. (1985). Oversmoothed nonparametric density estimates. Journal of the American Statistical Association, 80 : 209-214. | MR

[68] Turlach B.A. (1993). Bandwith selection in kernel density estimation : a review. Rapport technique, Université Catholique de Louvain.

[69] Wegkamp M.H. (1999). Quasi-universal bandwith selection for kernel density estimators A paraître dans The Canadian Journal of Statistics. | MR | Zbl

[70] Woodroofe M. (1970). On choosing a delta sequence. The Annals of Mathematical Statistics, 41 : 1665-1671. | MR | Zbl