@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://archive.numdam.org/item/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://archive.numdam.org/item/AIHPB_1989__25_4_533_0/
La convergence L1 et L infini de certains estimateurs d'une densité de probabilité, Thèse de Doctorat d'État, University Paris-VI, 1977.
,Statistical Estimation of Density Functions, Sankhya Series A, Vol. 25, 1963, pp. 245-254. | MR | Zbl
,An Alternative Method of Cross-Validation for the Smoothing of Density Estimates, Biometrika, Vol. 71, 1984, pp. 353-360. | MR
,Estimation des densités : risque minimax, Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, Vol. 47, 1979, pp. 119-137. | MR | Zbl
and ,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
, and ,A Data Dependent Approach to Density Estimation, Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, Vol. 69, 1985, pp. 609-628. | MR | Zbl
,Consistent Cross-Validated Density Estimation, Annals of Statistics, Vol. 11, 1983, pp. 25-38. | MR | Zbl
, and ,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
,A Course in Density Estimation, Birkhauser, Boston, 1987. | MR | Zbl
,The Kernel Estimate is Relatively Stable, Probability Theory and Related Fields, Vol. 77, 1988, pp. 521-536. | MR | Zbl
,A Universal Lower Bound for the Kernel Estimate, Statistics and Probability Letters, Vol. 0, 1988 (to appear). | MR | Zbl
,Asymptotic Performance Bounds for the Kernel Estimate, Annals of Statistics, Vol. 16, 1988, pp. 1162-1179. | MR | Zbl
,On the Non-Consistency of the L2 Cross-validated Kernel Density Estimate, 1988 (to appear). | MR | Zbl
,Nonparametric Density Estimation: The L1 View, John Wiley, New York, 1985. | MR | Zbl
and ,Distribution-Free Lower Bounds in Density Estimation, Annals of Statistics, Vol. 12, 1984, pp. 1250-1262. | MR | Zbl
and ,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
,Nonparametric Estimation of a Multivariate Probability Density, Theory of Probability and its Applications, Vol. 14, 1969, pp. 153-158. | Zbl
,Kernels for Nonparametric Curve Estimation, Journal of the Royal Statistical Society, Series B, Vol. 47, 1985, pp. 238-252. | MR | Zbl
, and ,A Stepwise Discriminant Analysis Program Using Density Estimation, in COMPSTAT 1974, G. BRUCKMAN Ed., pp. 101- 110, Physica Verlag, Wien, 1974. | MR
, and ,Cross-Validation in Density Estimation, Biometrika, Vol. 69, 1982, pp. 383-390. | MR | Zbl
,Large-Sample Optimality of Least Squares Cross-Validation in Density Estimation, Annals of Statistics, Vol. 11, 1983, pp. 1156-1174. | MR | Zbl
,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
,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
and ,Minimizing L1 Distance in Nonparametric Density Estimation, Journal of Multivariate Analysis, Vol. 26, 1988. pp. 59-88. | MR | Zbl
and ,Fourier Series, Cambridge University Press, 1962. | MR | Zbl
and ,Probability Inequalities for Sums of Bounded Random Variables, Journal of the American Statistical Association, Vol. 58, 1963, pp. 13-30. | MR | Zbl
,Smooth Optimum Kernel Estimators of Densities, Regression Curves and Modes, Annals of Statistics, Vol. 12, 1984, pp. 766-774. | MR | Zbl
,An Asymptotically Efficient Solution to the Bandwidth Problem of Kernel Density Estimation, Annals of Statistics, Vol. 13, 1985, pp. 1011-1023. | MR | Zbl
,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
,On the Estimation of a Probability Density Function and the Mode, Annals of Mathematical Statistics, Vol. 33, 1962, pp. 1065-1076. | MR | Zbl
,Remarks on Some Nonparametric Estimates of a Density Function, Annals of Mathematical Statistics, Vol. 27, 1956, pp. 832-837. | MR | Zbl
,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
,Empirical Choice of Histograms and Kernel Density Estimators, Scandinavian Journal of Statistics, Vol. 9, 1982, pp. 65-78. | MR | Zbl
,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.
and ,Biased and Unbiased Cross-Validation in Density Estimation, Journal of the American Statistical Association, Vol. 82, 1987, pp. 1131- 1146. | MR | Zbl
and ,Mean Squared Errors of Estimates of a Density and Its Derivatives, Biometrika, Vol. 66, 1979, pp. 177-180. | MR | Zbl
,An Asymptotically Optimal Window Selection Rule dor Kernel Density Estimates, Annals of Statistics, Vol. 12, 1984, pp. 1285-1297. | MR | Zbl
,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
and ,A Comparison Between two Kernel Estimators of a Probability Density Function and Its Derivatives, Scandinavian Actuarial Journal, Vol. 0, 1982, pp. 216-222.
, and ,On the Best Constants in the Khintchine Inequality, Studia Mathematica, Vol. 63, 1976, pp. 197-208. | MR | Zbl
,On the estimation of the Probability Density, Annals of Mathematical Statistics, Vol. 34, 1963, pp. 480-491. | MR | Zbl
and ,Measure and Integral, Marcel Dekker, New York, 1977. | MR | Zbl
and ,On Choosing a Delta Sequence, Annals of Mathematical Statistics, Vol. 41, 1970, pp. 1665-1671. | MR | Zbl
,