Estimation of nonlinear functionals revisited
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 14–1, Tome 363 (2009), pp. 126-138 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

After the overview of known results concerning estimating the linear and nonlinear functionals of the density for i.i.d. observations and for functionals of the signal observed in the White Gaussian Noise (WGN) with small intensity we consider the similar problems for the observation the Poisson random process. Asymptotically efficient estimates of the once Frechet differentiable functionals are proposed. Bibl. – 10 titles.
@article{ZNSL_2009_363_a6,
     author = {R. Khasminskii},
     title = {Estimation of nonlinear functionals revisited},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {126--138},
     year = {2009},
     volume = {363},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_363_a6/}
}
TY  - JOUR
AU  - R. Khasminskii
TI  - Estimation of nonlinear functionals revisited
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2009
SP  - 126
EP  - 138
VL  - 363
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2009_363_a6/
LA  - en
ID  - ZNSL_2009_363_a6
ER  - 
%0 Journal Article
%A R. Khasminskii
%T Estimation of nonlinear functionals revisited
%J Zapiski Nauchnykh Seminarov POMI
%D 2009
%P 126-138
%V 363
%U http://geodesic.mathdoc.fr/item/ZNSL_2009_363_a6/
%G en
%F ZNSL_2009_363_a6
R. Khasminskii. Estimation of nonlinear functionals revisited. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 14–1, Tome 363 (2009), pp. 126-138. http://geodesic.mathdoc.fr/item/ZNSL_2009_363_a6/

[1] G. K. Gobulev, “Nonparametric estimation of smooth densities of a distribution in $L_2$”, Problems Inform. Transmission, 28:1 (1992), 44–54 | MR

[2] R. Hasminskii, I. Ibragimov, “On the nonparametric estimation of functionals”, Proc. II Prague Symp. Asymptotic Statistics, 1978, 41–51 | MR

[3] R. Hasminskii, I. Ibragimov, “On density estimation in the view of Kolmogorov's ideas in approximation theory”, Annals Statist., 18 (1990), 999–1010 | DOI | MR | Zbl

[4] I. Ibragimov, R. Khasminskii, Statistical Estimation: Asymptotic Theory, Springer-Verlag, 1981 | MR | Zbl

[5] I. Ibragimov, A. Nemirovski, R. Khasminskii, “Some problems of nonparametric estimation in Gaussian white noise”, Theory Probab. Appl., 31:3 (1986), 391–406 | DOI | MR

[6] Yu. Kutoyants, Statistical Inference for Spatial Poisson Processes, Lect. Notes Statistics, 134, Springer, 1998 | DOI | MR | Zbl

[7] B. Levit, “On optimality of some statistical estimates”, Proc. Prague Symp. Asymptotic Statistics, 1973, 215–238 | MR

[8] B. Levit, “On the efficiency of a class of nonparametric estimates”, Theor. Probab. Applic., 20 (1975), 723–740 | DOI | MR | Zbl

[9] A. Nemirovski, “Topics in Nonparametric Statistics”, M. Emery, A. Nemirovski, D. Voiculescu, Lectures on Probability Theory and Statistics, Ecole d'ete de Probabilities (Saint-Flour XXVIII, 1998), Lect. Notes Math., 1738, ed. P. Bernard, Springer, 2000, 85–277 | MR | Zbl

[10] S. Ross, Introduction to Probability Models, 9th edition, Academic Press, 2006