no. 4
The double kernel method in density estimation
Annales de l'I.H.P. Probabilités et statistiques, Tome 25 (1989) no. 4, pp. 533-580. 
@article{AIHPB_1989__25_4_533_0,
     author = {Devroye, Luc},
     title = {The double kernel method in density estimation},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {533--580},
     publisher = {Gauthier-Villars},
     volume = {25},
     number = {4},
     year = {1989},
     mrnumber = {1045250},
     zbl = {0701.62044},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1989__25_4_533_0/}
}
TY  - JOUR
AU  - Devroye, Luc
TI  - The double kernel method in density estimation
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 1989
SP  - 533
EP  - 580
VL  - 25
IS  - 4
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPB_1989__25_4_533_0/
LA  - en
ID  - AIHPB_1989__25_4_533_0
ER  - 
%0 Journal Article
%A Devroye, Luc
%T The double kernel method in density estimation
%J Annales de l'I.H.P. Probabilités et statistiques
%D 1989
%P 533-580
%V 25
%N 4
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPB_1989__25_4_533_0/
%G en
%F AIHPB_1989__25_4_533_0
Devroye, Luc. The double kernel method in density estimation. Annales de l'I.H.P. Probabilités et statistiques, Tome 25 (1989) no. 4, pp. 533-580. http://www.numdam.org/item/AIHPB_1989__25_4_533_0/

S. Abou-Jaoude, La convergence L1 et L infini de certains estimateurs d'une densité de probabilité, Thèse de Doctorat d'État, University Paris-VI, 1977.

M.S. Bartlett, Statistical Estimation of Density Functions, Sankhya Series A, Vol. 25, 1963, pp. 245-254. | MR | Zbl

A.W. Bowman, An Alternative Method of Cross-Validation for the Smoothing of Density Estimates, Biometrika, Vol. 71, 1984, pp. 353-360. | MR

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

M. Broniatowski, P. Deheuvels and L. Devroye, On the relationship Between Stability of Extreme Order Statistics and Convergence of the Maximum Likelihood Kernel Density Estimate, Annals of Statistics, Vol. 0, 1988, pp. 0-0 (to appear). | MR | Zbl

P. Burman, A Data Dependent Approach to Density Estimation, Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, Vol. 69, 1985, pp. 609-628. | MR | Zbl

Y.S. Chow, S. Geman and L.D.. Wu, Consistent Cross-Validated Density Estimation, Annals of Statistics, Vol. 11, 1983, pp. 25-38. | MR | Zbl

L. Devroye, The Equivalence of Weak, Strong and Complete Convergence in L1 for Kernel Density Estimates, Annals of Statistics, Vol. 11, 1983, pp. 896-904. | MR | Zbl

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

L. Devroye, The Kernel Estimate is Relatively Stable, Probability Theory and Related Fields, Vol. 77, 1988, pp. 521-536. | MR | Zbl

L. Devroye, A Universal Lower Bound for the Kernel Estimate, Statistics and Probability Letters, Vol. 0, 1988 (to appear). | MR | Zbl

L. Devroye, Asymptotic Performance Bounds for the Kernel Estimate, Annals of Statistics, Vol. 16, 1988, pp. 1162-1179. | MR | Zbl

L. Devroye, On the Non-Consistency of the L2 Cross-validated Kernel Density Estimate, 1988 (to appear). | MR | Zbl

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

L. Devroye and C.S. Penrod, Distribution-Free Lower Bounds in Density Estimation, Annals of Statistics, Vol. 12, 1984, pp. 1250-1262. | MR | Zbl

R.P.W. Duin, On the Choice of Smoothing Parameters for Parzen Estimators of Probability Density Functions, I.E.E.E. Transactions on Computers, Vol. C-25, 1976, pp. 1175- 1179. | Zbl

V.A. Epanechnikov, Nonparametric Estimation of a Multivariate Probability Density, Theory of Probability and its Applications, Vol. 14, 1969, pp. 153-158. | Zbl

T. Gasser, H.-G. Müller and V. Mammitzsch, Kernels for Nonparametric Curve Estimation, Journal of the Royal Statistical Society, Series B, Vol. 47, 1985, pp. 238-252. | MR | Zbl

J.D.F. Habbema, J. Hermans and K. Vandenbroek, A Stepwise Discriminant Analysis Program Using Density Estimation, in COMPSTAT 1974, G. BRUCKMAN Ed., pp. 101- 110, Physica Verlag, Wien, 1974. | MR

P. Hall, Cross-Validation in Density Estimation, Biometrika, Vol. 69, 1982, pp. 383-390. | MR | Zbl

P. Hall, Large-Sample Optimality of Least Squares Cross-Validation in Density Estimation, Annals of Statistics, Vol. 11, 1983, pp. 1156-1174. | MR | Zbl

P. Hall, Asymptotic Theory of Minimum Integrated Square Error for Multivariate Density Estimation, in Multivariate Analysis VI, P. R. KRISHNAIAH Ed., pp. 289-309, North-Holland, Amsterdam, 1985. | MR | Zbl

P. Hall and 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, 1987, pp. 567-581. | MR | Zbl

P. Hall and M.P. Wand, Minimizing L1 Distance in Nonparametric Density Estimation, Journal of Multivariate Analysis, Vol. 26, 1988. pp. 59-88. | MR | Zbl

G.H. Hardy and W.W. Rogosinski, Fourier Series, Cambridge University Press, 1962. | MR | Zbl

W. Hoeffding, Probability Inequalities for Sums of Bounded Random Variables, Journal of the American Statistical Association, Vol. 58, 1963, pp. 13-30. | MR | Zbl

H.-G. Müller, Smooth Optimum Kernel Estimators of Densities, Regression Curves and Modes, Annals of Statistics, Vol. 12, 1984, pp. 766-774. | MR | Zbl

J.S. Marron, An Asymptotically Efficient Solution to the Bandwidth Problem of Kernel Density Estimation, Annals of Statistics, Vol. 13, 1985, pp. 1011-1023. | MR | Zbl

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, 1974, pp. 133-141. | Zbl

E. Parzen, On the Estimation of a Probability Density Function and the Mode, Annals of Mathematical Statistics, Vol. 33, 1962, pp. 1065-1076. | MR | Zbl

M. Rosenblatt, Remarks on Some Nonparametric Estimates of a Density Function, Annals of Mathematical Statistics, Vol. 27, 1956, pp. 832-837. | MR | Zbl

M. Rosenblatt, Global Measures of Deviation for Kernel and Nearest Neighbor Density Estimates, in Proceedings of the Heidelberg Workshop, pp. 181-190, Springer-Verlag, Berlin, 1979. | MR | Zbl

M. Rudemo, Empirical Choice of Histograms and Kernel Density Estimators, Scandinavian Journal of Statistics, Vol. 9, 1982, pp. 65-78. | MR | Zbl

E.F. Schuster and G.G. Gregory, On the Nonconsistency of Maximum Likelihood Nonparametric Density Estimators, in Computer Science and Statistics: Proceedings of the 13th Symposium on the Interface, W. F. EDDY Ed., pp. 295-298, Springer Verlag, New York, N.Y., 1981.

D.W. Scott and G.R. Terrell, Biased and Unbiased Cross-Validation in Density Estimation, Journal of the American Statistical Association, Vol. 82, 1987, pp. 1131- 1146. | MR | Zbl

R.S. Singh, Mean Squared Errors of Estimates of a Density and Its Derivatives, Biometrika, Vol. 66, 1979, pp. 177-180. | MR | Zbl

C.J. Stone, An Asymptotically Optimal Window Selection Rule dor Kernel Density Estimates, Annals of Statistics, Vol. 12, 1984, pp. 1285-1297. | MR | Zbl

W. Stuetzle and Y. Mittal, Some Comments on the Asymptotic Behavior of Robust Smoothers, in Proceedings of the Heidelberg Worskshop, T. GASSER and M. ROSENBLATT Eds., pp. 191-195, Springer-Verlag, Heidelberg, 1979. | MR | Zbl

H.Y.. Su-Wong, B. Prasad and R.S. Singh, A Comparison Between two Kernel Estimators of a Probability Density Function and Its Derivatives, Scandinavian Actuarial Journal, Vol. 0, 1982, pp. 216-222.

S.J. Szarek, On the Best Constants in the Khintchine Inequality, Studia Mathematica, Vol. 63, 1976, pp. 197-208. | MR | Zbl

G.S. Watson and M.R. Leadbetter, On the estimation of the Probability Density, Annals of Mathematical Statistics, Vol. 34, 1963, pp. 480-491. | MR | Zbl

R.L. Wheeden and A. Zygmund, Measure and Integral, Marcel Dekker, New York, 1977. | MR | Zbl

M. Woodroofe, On Choosing a Delta Sequence, Annals of Mathematical Statistics, Vol. 41, 1970, pp. 1665-1671. | MR | Zbl