Une mesure de la déviation quadratique d'estimateurs non paramétriques
P. Doukhan; J. Leon; F. Portal
Annales de l'I.H.P. Probabilités et statistiques (1986)
- Volume: 22, Issue: 1, page 37-66
- ISSN: 0246-0203
Access Full Article
topHow to cite
topDoukhan, P., Leon, J., and Portal, F.. "Une mesure de la déviation quadratique d'estimateurs non paramétriques." Annales de l'I.H.P. Probabilités et statistiques 22.1 (1986): 37-66. <http://eudml.org/doc/77269>.
@article{Doukhan1986,
author = {Doukhan, P., Leon, J., Portal, F.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {kernel-type estimator; density estimation; nonparametric regression; mean square error; asymptotic normality; orthogonal series estimator; Gaussian distribution; mixing; Gaussian approximations; Hilbert spaces; Karhunen- Loeve expansion},
language = {fre},
number = {1},
pages = {37-66},
publisher = {Gauthier-Villars},
title = {Une mesure de la déviation quadratique d'estimateurs non paramétriques},
url = {http://eudml.org/doc/77269},
volume = {22},
year = {1986},
}
TY - JOUR
AU - Doukhan, P.
AU - Leon, J.
AU - Portal, F.
TI - Une mesure de la déviation quadratique d'estimateurs non paramétriques
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1986
PB - Gauthier-Villars
VL - 22
IS - 1
SP - 37
EP - 66
LA - fre
KW - kernel-type estimator; density estimation; nonparametric regression; mean square error; asymptotic normality; orthogonal series estimator; Gaussian distribution; mixing; Gaussian approximations; Hilbert spaces; Karhunen- Loeve expansion
UR - http://eudml.org/doc/77269
ER -
References
top- [1] J. Bretagnolle, C. Huber, Estimation des densités : risques minimaux. Z. W., t. 47, 1979, p. 119-137. Zbl0413.62024MR523165
- [2] N.N. Cencov, Evaluations of unknown distribution density from observation. Soviet. Math., t. 3, 1962, p. 1559-1562. Zbl0133.11801
- [3] G. Collomb, Thèse. Université Paul Sabatier, Toulouse, 1976.
- [4] G. Collomb, P. Doukhan, C. R. A. S. Série I, t. 296, 1983, p. 859-862. Zbl0529.62037MR712758
- [5] M. Csörgö, P. Revesz, Strong approximations in Probability and Statistics, 1981, Academic Press. Zbl0539.60029MR666546
- [6] H. Dehling, Limit theorems for sums of weakly dependant Banach space valued random variables. Z. W., t. 63, 1983, p. 393-432. Zbl0496.60004MR705631
- [7] P. Doukhan, Simulations in the first order autogression process. Specifying Statistical Models. Lecture Notes in Statistics, t. 16, 1983, p. 50-68, Spinger-Verlag. Zbl0503.62085
- [8] P. Doukhan, J. León and F. Portal, C. R. A. S. Série I., 1984.
- [9] P. Doukhan, J. León and F. Portal, Calcul de la vitesse de convergence dans le théorème central limite, vis-à-vis des distances de Levy, Dudley et Prohorov, dans le cas de variables aléatoires dépendantes (Probability and Mathematical Statistics, Vol. 6, Fasc. 1), 1985. Zbl0607.60019
- [10] P. Doukhan, J. León and F. Portal, Applications Statistiques des principes d'Invariance dans un cadre mélangeant, 1984 (à paraître).
- [11] P. Doukhan, F. Portal, C. R. A. S. Série I, t. 297, 1983, p. 129-132. Zbl0544.62022MR720925
- [12] T. Gasser and H.G. Muller, Kernel estimations of regression functions, Smoothing technics for curve estimation. Lecture Notes in Mathematics, t. 757, 1979, p. 23-68, Springer-Verlag. Zbl0418.62033MR564251
- [13] W. Greblicki, D. Rutowska and L. Rutowski, An orthogonal series estimate of time varying regression. Ann. Inst. Stat. Math. A, t. 35, 1983, p. 215-228. Zbl0536.62072MR716032
- [14] J. Kuelbs and T. Kurtz, Berry Essen estimates in Hilbert space an application to L. I. L. Ann. Prob., t. 2, 1974, p. 387-407. Zbl0298.60017MR362427
- [15] J. León, Asymptotic behaviour of the quadratic deviation of multivariante density estimates. Ann. Inst. Henry Poincaré B, t. 19, 1983, p. 297-309. Zbl0527.62046MR725562
- [16] E.J. Parzen, On estimation of a Probability Density andMode. Ann. Math., t. 35, 1962, p. 1065-1076. Zbl0116.11302
- [17] M. Reed and B. Simon, Methods of modern Mathematical Physics, t. III, 1970, Academic Press. Zbl0405.47007
- [18] M. Rosenblatt, A quadratic measure of deviation of two dimensional density estimates and a test of independence. Ann. of Stat., t. 3, 1975, p. 1-14. Zbl0325.62030MR428579
- [19] G. Sansone, Orthogonal functions, Interscience Publisher Inc., New York, 1959. Zbl0084.06106MR103368
- [20] S.C. Schwartz, Estimation of a probability density by an orthogonal serie. Ann. Math. Stat., t. 38, 1967, p. 1261-1265. Zbl0157.47904MR221638
- [21] G. Szegö, Orthogonal Polynomials. Amer. Math. Soc. Coll. Publ., t. 23, 1959. Zbl0089.27501MR106295
- [22] H. Takahata, L∞-bound for asymptotic normality of weakly dependent summands using Stein's result. Ann. Prob., t. 9, 1981, p. 676. Zbl0465.60033MR624695
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.