@article{SAD_1989__14_1_1_0, author = {Berlinet, Alain and Devroye, Luc}, title = {Estimation d'une densit\'e : un point sur la m\'ethode du noyau}, journal = {Statistique et analyse des donn\'ees}, pages = {1--32}, publisher = {Association pour la statistique et ses illustrations}, volume = {14}, number = {1}, year = {1989}, language = {fr}, url = {http://archive.numdam.org/item/SAD_1989__14_1_1_0/} }
TY - JOUR AU - Berlinet, Alain AU - Devroye, Luc TI - Estimation d'une densité : un point sur la méthode du noyau JO - Statistique et analyse des données PY - 1989 SP - 1 EP - 32 VL - 14 IS - 1 PB - Association pour la statistique et ses illustrations UR - http://archive.numdam.org/item/SAD_1989__14_1_1_0/ LA - fr ID - SAD_1989__14_1_1_0 ER -
%0 Journal Article %A Berlinet, Alain %A Devroye, Luc %T Estimation d'une densité : un point sur la méthode du noyau %J Statistique et analyse des données %D 1989 %P 1-32 %V 14 %N 1 %I Association pour la statistique et ses illustrations %U http://archive.numdam.org/item/SAD_1989__14_1_1_0/ %G fr %F SAD_1989__14_1_1_0
Berlinet, Alain; Devroye, Luc. Estimation d'une densité : un point sur la méthode du noyau. Statistique et analyse des données, Estimation fonctionnelle, Tome 14 (1989) no. 1, pp. 1-32. http://archive.numdam.org/item/SAD_1989__14_1_1_0/
Convergence uniforme presque sûre d'une classe d'estimateurs à noyau, pour la densité. Comptes Rendus de l'Académie des Sciences de Paris, vol. 303, pp. 761-764, 1986. | MR | Zbl
etDeux remarques sur l'estimation. Comptes Rendus de l'Académie des Sciences de Paris, vol. 296, pp. 1021-1024, 1983. | MR | Zbl
Propriétés locales d'un paramètre. Application à l'estimation. Comptes Rendus de l'Académie des Sciences de Paris, vol. 298, pp. 345-348, 1984. | MR | Zbl
Simulating to forecast. The Eighth International Symposium on Forecasting, Amsterdam, June 12-15, 1988.
Non-asymptotic minimax risk for Hellinger balls. Probability and Mathematical Statistics, Vol. 5, pp. 21-29, 1985. | MR | Zbl
On estimating a density using Hellinger distance and some other strange facts. Probability Theory and Related Fields, vol. 71, pp. 271-291, 1986 | MR | Zbl
On the risk of histograms for estimating decreasing densities. Annals of Statistics, vol 15, pp.1013-1022, 1987a. | MR | Zbl
Estimating a density under order restrictions : non-asymptotic minimax risk. Annals of Statistics, vol 15, pp. 995-1012, 1987b. | MR | Zbl
Théorie de l'Estimation Fonctionnelle, Economica, Paris, 1987.
etAn alternative method of cross-validation for the smoothing of density estimates. Biometrika, vol. 71, pp. 353-360, 1984. | MR
Estimation des densités : risque minimax. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, vol. 47, pp. 119-137, 1979. | MR | Zbl
etA data dependent approach to density estimation. Zeitschrift für Wahrscheinlichkeitstheorie undverwandte Gebiete, vol. 69, pp. 609-628, 1985. | MR | Zbl
Consistent cross-validated density estimation. Annals of Statistics, vol. 11, pp. 25-38, 1983. | MR | Zbl
, etMean integrated square error properties of density estimates. Annals of Statistics, vol. 5, pp. 530-535, 1977. | MR | Zbl
Estimation non-paramétrique de la densité par histogrammes généralisés. Revue de Statistique Appliquée, vol. 25, pp. 5-42, 1977a. | Numdam | MR
Estimation non-paramétrique de la densité par histogrammes généralisés (II). Publications de l'Institut de Statistique des Universités de Paris, vol. 22,pp. 1-23, 1977b. | MR | Zbl
The equivalence of weak, strong and complete convergence in L1 for kernel density estimates. Annals of Statistics, vol. 11, pp. 896-904, 1983. | MR | Zbl
Non-Uniform Random Variate Generation Springer-Verlag, 1986. | MR | Zbl
Nonparametric density estimates with improved performance on given sets of densities. Statistics ( Mathematische Operationsforschung und Statistik ) , 1986, to appear. | MR | Zbl
A Course in Density Estimation. Birkhauser, Boston, 1987a. | MR | Zbl
An application of the Efron-Stein inequality in density estimation. Annals of Statistics, vol. 15, pp. 1317-1320, 1987b. | MR | Zbl
An L1 asymptotically optimal kernel estimate. Technical Report, McGill University, Montréal, 1987c.
Asymptotic performance bounds for the kernel estimate. Annals of Statistics, vol. 16, pp. 1162-1179, 1988a. | MR | Zbl
The kernel estimate is relatively stable. Probability Theory and Related Fields, vol. 77, pp. 521-536, 1988b. | MR | Zbl
Nonparametric Density Estimation : The L1 View. John Wiley, New York, 1985. | MR | Zbl
etDistribution-free lower bounds in density estimation. Annals of Statistics, vol. 12, pp. 1250-1262, 1984. | MR | Zbl
etOn the choice of smoothing parameters for Parzen estimators of probability density functions. IEEE Transactions on Computers, vol. C-25, pp. 1175-1179, 1976. | Zbl
On the theory of mortality measurement, part II. Skandinavisk Aktuarietidskrift, vol. 39, pp. 125-153, 1956. | MR | Zbl
A stepwise discriminant analysis program using density estimation, in COMPSTAT 1974, ed. G. Bruckmann, pp. 101-110, Physica-Verlag, Wien, 1974. | MR | Zbl
, etCross-validation in density estimation. Biometrika, vol. 69, pp. 383-390, 1982. | MR | Zbl
Large-sample optimality of least squares cross-validation in density estimation. Annals of Statistics, vol. 11, pp. 1156-1174, 1983. | MR | Zbl
Asymptotic theory of minimum integrated square error for multivariate density estimation. Multivariate Analysis VI, ed. Krishnaiah, pp. 289-309, North-Holland, Amsterdam, 1985. | MR | Zbl
Extent to which least-squares cross-validation minimises integrated square error in nonparametric density estimation. Probability Theory and Related Fields, vol. 74, pp. 567-581, 1987a. | MR | Zbl
etChoice of kernel order in density estimation. Annals of Statistics, vol. 16, pp. 161-173, 1987b. | MR | Zbl
etMinimizing L1 distance in nonparametric density estimation. Journal of Multivariate Analysis, 1988, to appear. | MR | Zbl
andEstimation of distribution density belonging to a class of entire functions.Theory of Probability and its Applications, vol. 17, pp. 551-562, 1982. | Zbl
etAn asymptotically efficient solution to the bandwith problem of kernel density estimation. Annals of Statistics, vol. 13, pp. 1011-1023, 1985. | MR | Zbl
On the integral mean square error of some nonparametric estimates for the density function. Theory of Probability and its Applications, vol. 19, pp. 133-141, 1974. | Zbl
A semiparametric approach to density estimation. Journal of the American Statistical Association, vol. 82, pp. 858-865, 1987. | MR | Zbl
etOn the estimation of a probability density function and the mode. Annals of Mathematical Statistics, vol. 33, pp. 1065-1076, 1962. | MR | Zbl
Remarks on some nonparametric estimates of a density function. Annals of Mathematical Statistics, vol. 27, pp. 832-837, 1956. | MR | Zbl
Empirical choice of histograms and kernel density estimators. Scandinavian Journal of Statistics, vol. 9, pp. 65-78, 1982. | MR | Zbl
A useful convergence theorem for probability distribution. Annals of Mathematical Statistics, vol. 18, pp. 434-438, 1947. | MR | Zbl
On the nonconsistency of maximum likelihood nonparametric density estimators. Computer Science and Statistics : Proceedings of the 13th Symposium on the Interface, ed. W.F. Eddy, pp.295-298, Springer-Verlag, New York, 1981.
etParametric / nonparametric mixture density estimation with application to flood frequency analysis. Water Resources Bulletin, vol. 21, pp. 797-804, 1985.
etBiased and unbiased cross-validation in density estimation. Journal of the American Statistical Association, vol. 82,pp. 1131-1146, 1987. | MR | Zbl
etDensity Estimation for Statistics and Data Analysis. Chapman et Hall, Londres, 1986. | MR | Zbl
An asymptotically optimal window selection rule for kernel density estimates. Annals of Statistics, vol. 12, pp. 1285-1297, 1984. | MR | Zbl
An asymptotically optimal histogram selection rule. Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer, vol. 2, ed. L. Le Cam et R.A. Olshen, pp. 513-520, Wadsworth, Belmont, 1985. | MR
Some comments on the asymptotic behavior of robust smoothers. Proceedings of the Heidelberg Workshop, ed. T. Gasser et M. Rosenblatt, pp. 191-195, Springer-Verlag, Heidelberg, 1979. | MR | Zbl
etNonparametric Probability Density Estimation, Johns Hopkins University Press, Baltimore, 1978. | MR | Zbl
etOn the estimation of the probability density. Annals of Mathematical Statistics, vol. 34, pp. 480-491, 1963. | MR | Zbl
etOn choosing a delta sequence. Annals of Mathematical Statistics, vol. 41, pp. 1665-1671, 1970. | MR | Zbl