Asymptotic behaviour of the quadratic measure of deviation of multivariate density estimates
Annales de l'I.H.P. Probabilités et statistiques, Volume 19 (1983) no. 3, p. 297-309
@article{AIHPB_1983__19_3_297_0,
     author = {Le\'on, Jos\'e Rafael},
     title = {Asymptotic behaviour of the quadratic measure of deviation of multivariate density estimates},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {19},
     number = {3},
     year = {1983},
     pages = {297-309},
     zbl = {0527.62046},
     mrnumber = {725562},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1983__19_3_297_0}
}
Leon R., José Rafael. Asymptotic behaviour of the quadratic measure of deviation of multivariate density estimates. Annales de l'I.H.P. Probabilités et statistiques, Volume 19 (1983) no. 3, pp. 297-309. http://www.numdam.org/item/AIHPB_1983__19_3_297_0/

[1] P.J. Bickel and M. Rosenblatt, On some measures of the deviations of density functions estimates. The Ann. of Statistics, t. 1, n° 6, 1973, p. 1071-1095. | MR 348906 | Zbl 0275.62033

[2] N.N. Cencov, Evaluations of an unknown distribution density from observations. Soviet Math., t. 3, 1962, p. 1559-1562. | Zbl 0133.11801

[3] R. Courant and D. Hilbert, Methods of Mathematical Physics, t. 1, New York, 1953.

[4] E. Giné, J. León, On the central limit theorem in Hilbert Spaces. Stochastica, t. IV, n° 1, 1980, p. 43-71. | MR 573725 | Zbl 0432.60011

[5] U. Grenander, Szegö. Toeplitz forms and their application. University of California Press. Berkeley. 1958. | MR 94840 | Zbl 0080.09501

[6] E. Isaccson, H. Keller, « Analysis of Numerical Methods » John Wiley and Sons. Inc. New York, 1966. | MR 201039 | Zbl 0168.13101

[7] Kuelbs, Kurtz, Bery Essen estimates in Hilbert Space and an application to the LIL. Ann. Probability, t. 2, 1974, p. 387-407. | MR 362427 | Zbl 0298.60017

[8] E.A. Naradaya, On a quadratic measure of deviation of the estimate of a distribution density. Theo. Prob. and its App., n° 4, 1976, p. 844-850. | Zbl 0385.62020

[9] A. Zygmund, Trygonometric series, 2nd Ed. Cambridge University Press. New York, 1959. | MR 107776 | Zbl 0085.05601