Geodesic
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.

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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://geodesic.mathdoc.fr/item/SAD_1989__14_1_1_0/

B. Abdous et A. Berlinet 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. | Zbl | MR

P. Assouad Deux remarques sur l'estimation. Comptes Rendus de l'Académie des Sciences de Paris, vol. 296, pp. 1021-1024, 1983. | Zbl | MR

A. Berlinet Propriétés locales d'un paramètre. Application à l'estimation. Comptes Rendus de l'Académie des Sciences de Paris, vol. 298, pp. 345-348, 1984. | Zbl | MR

A. Berlinet Simulating to forecast. The Eighth International Symposium on Forecasting, Amsterdam, June 12-15, 1988.

L. Birgé Non-asymptotic minimax risk for Hellinger balls. Probability and Mathematical Statistics, Vol. 5, pp. 21-29, 1985. | Zbl | MR

L. Birgé On estimating a density using Hellinger distance and some other strange facts. Probability Theory and Related Fields, vol. 71, pp. 271-291, 1986 | Zbl | MR

L. Birgé On the risk of histograms for estimating decreasing densities. Annals of Statistics, vol 15, pp.1013-1022, 1987a. | Zbl | MR

L. Birgé Estimating a density under order restrictions : non-asymptotic minimax risk. Annals of Statistics, vol 15, pp. 995-1012, 1987b. | Zbl | MR

D. Bosq et J.P. Lecoutre Théorie de l'Estimation Fonctionnelle, Economica, Paris, 1987.

A.W. Bowman An alternative method of cross-validation for the smoothing of density estimates. Biometrika, vol. 71, pp. 353-360, 1984. | MR

J. Bretagnolle et C. Huber Estimation des densités : risque minimax. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, vol. 47, pp. 119-137, 1979. | Zbl | MR

P. Burman A data dependent approach to density estimation. Zeitschrift für Wahrscheinlichkeitstheorie undverwandte Gebiete, vol. 69, pp. 609-628, 1985. | Zbl | MR

Y.S. Chow, S. Geman et L.D. Wu Consistent cross-validated density estimation. Annals of Statistics, vol. 11, pp. 25-38, 1983. | Zbl | MR

K.B. Davis Mean integrated square error properties of density estimates. Annals of Statistics, vol. 5, pp. 530-535, 1977. | Zbl | MR

P. Deheuvels Estimation non-paramétrique de la densité par histogrammes généralisés. Revue de Statistique Appliquée, vol. 25, pp. 5-42, 1977a. | MR | mathdoc-id

P. Deheuvels 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. | Zbl | MR

L. Devroye The equivalence of weak, strong and complete convergence in L1 for kernel density estimates. Annals of Statistics, vol. 11, pp. 896-904, 1983. | Zbl | MR

L. Devroye Non-Uniform Random Variate Generation Springer-Verlag, 1986. | Zbl | MR

L. Devroye Nonparametric density estimates with improved performance on given sets of densities. Statistics ( Mathematische Operationsforschung und Statistik ) , 1986, to appear. | Zbl | MR

L. Devroye A Course in Density Estimation. Birkhauser, Boston, 1987a. | Zbl | MR

L. Devroye An application of the Efron-Stein inequality in density estimation. Annals of Statistics, vol. 15, pp. 1317-1320, 1987b. | Zbl | MR

L. Devroye An L1 asymptotically optimal kernel estimate. Technical Report, McGill University, Montréal, 1987c.

L. Devroye Asymptotic performance bounds for the kernel estimate. Annals of Statistics, vol. 16, pp. 1162-1179, 1988a. | Zbl | MR

L. Devroye The kernel estimate is relatively stable. Probability Theory and Related Fields, vol. 77, pp. 521-536, 1988b. | Zbl | MR

L. Devroye et L. Györfi Nonparametric Density Estimation : The L1 View. John Wiley, New York, 1985. | Zbl | MR

L. Devroye et C.S. Penrod Distribution-free lower bounds in density estimation. Annals of Statistics, vol. 12, pp. 1250-1262, 1984. | Zbl | MR

R.P.W. Duin On the choice of smoothing parameters for Parzen estimators of probability density functions. IEEE Transactions on Computers, vol. C-25, pp. 1175-1179, 1976. | Zbl

U. Grenander On the theory of mortality measurement, part II. Skandinavisk Aktuarietidskrift, vol. 39, pp. 125-153, 1956. | Zbl | MR

J.D.F. Habbema, J. Hermans et K. Vandenbroek A stepwise discriminant analysis program using density estimation, in COMPSTAT 1974, ed. G. Bruckmann, pp. 101-110, Physica-Verlag, Wien, 1974. | Zbl | MR

P. Hall Cross-validation in density estimation. Biometrika, vol. 69, pp. 383-390, 1982. | Zbl | MR

P. Hall Large-sample optimality of least squares cross-validation in density estimation. Annals of Statistics, vol. 11, pp. 1156-1174, 1983. | Zbl | MR

P. Hall Asymptotic theory of minimum integrated square error for multivariate density estimation. Multivariate Analysis VI, ed. Krishnaiah, pp. 289-309, North-Holland, Amsterdam, 1985. | Zbl | MR

P. Hall et J.S. Marron 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. | Zbl | MR

P. Hall et J.S. Marron Choice of kernel order in density estimation. Annals of Statistics, vol. 16, pp. 161-173, 1987b. | Zbl | MR

P. Hall and M.P. Wand Minimizing L1 distance in nonparametric density estimation. Journal of Multivariate Analysis, 1988, to appear. | Zbl | MR

I. A. Ibragimov et R.Z. Khas'Minskii Estimation of distribution density belonging to a class of entire functions.Theory of Probability and its Applications, vol. 17, pp. 551-562, 1982. | Zbl

J.S. Marron An asymptotically efficient solution to the bandwith problem of kernel density estimation. Annals of Statistics, vol. 13, pp. 1011-1023, 1985. | Zbl | MR

E.A. Nadaraya 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

I. Olkin et C.H. Spiegelman A semiparametric approach to density estimation. Journal of the American Statistical Association, vol. 82, pp. 858-865, 1987. | Zbl | MR

E. Parzen On the estimation of a probability density function and the mode. Annals of Mathematical Statistics, vol. 33, pp. 1065-1076, 1962. | Zbl | MR

M. Rosenblatt Remarks on some nonparametric estimates of a density function. Annals of Mathematical Statistics, vol. 27, pp. 832-837, 1956. | Zbl | MR

M. Rudemo Empirical choice of histograms and kernel density estimators. Scandinavian Journal of Statistics, vol. 9, pp. 65-78, 1982. | Zbl | MR

H. Scheffé A useful convergence theorem for probability distribution. Annals of Mathematical Statistics, vol. 18, pp. 434-438, 1947. | Zbl | MR

E.F. Schuster et G.G. Gregory 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.

E.F. Schuster et S. Yakowitz Parametric / nonparametric mixture density estimation with application to flood frequency analysis. Water Resources Bulletin, vol. 21, pp. 797-804, 1985.

D.W. Scott et G.R. Terrell Biased and unbiased cross-validation in density estimation. Journal of the American Statistical Association, vol. 82,pp. 1131-1146, 1987. | Zbl | MR

B.W. Silverman Density Estimation for Statistics and Data Analysis. Chapman et Hall, Londres, 1986. | Zbl | MR

C.J. Stone An asymptotically optimal window selection rule for kernel density estimates. Annals of Statistics, vol. 12, pp. 1285-1297, 1984. | Zbl | MR

C.J. Stone 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

W. Stuetzle et Y. Mittal 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. | Zbl | MR

R.A. Tapia et J.R. Thompson Nonparametric Probability Density Estimation, Johns Hopkins University Press, Baltimore, 1978. | Zbl | MR

G.S. Watson et M.R. Leadbetter On the estimation of the probability density. Annals of Mathematical Statistics, vol. 34, pp. 480-491, 1963. | Zbl | MR

M. Woodroofe On choosing a delta sequence. Annals of Mathematical Statistics, vol. 41, pp. 1665-1671, 1970. | Zbl | MR