Geodesic
Estumation of density on indirect observation
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 17, Tome 396 (2011), pp. 204-212 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In this paper it is investigated the accuracy of the estimating of the unknown density in the $L_1$-space on indirect observation. We suggest a simple nonparametric estimator $\widehat f_n$ for unknown density $f$ and under some appropriate conditions prove the consistency of this estimator. 
@article{ZNSL_2011_396_a13,
     author = {V. N. Solev},
     title = {Estumation of density on indirect observation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {204--212},
     year = {2011},
     volume = {396},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_396_a13/}
}
TY  - JOUR
AU  - V. N. Solev
TI  - Estumation of density on indirect observation
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2011
SP  - 204
EP  - 212
VL  - 396
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2011_396_a13/
LA  - ru
ID  - ZNSL_2011_396_a13
ER  - 
%0 Journal Article
%A V. N. Solev
%T Estumation of density on indirect observation
%J Zapiski Nauchnykh Seminarov POMI
%D 2011
%P 204-212
%V 396
%U http://geodesic.mathdoc.fr/item/ZNSL_2011_396_a13/
%G ru
%F ZNSL_2011_396_a13
V. N. Solev. Estumation of density on indirect observation. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 17, Tome 396 (2011), pp. 204-212. http://geodesic.mathdoc.fr/item/ZNSL_2011_396_a13/

[1] P. Massart, “The tight constant in the Dvoretzky–Kiefer–Wolfowitz inequality”, Ann. Probab., 18 (1990), 1269–1283 | DOI | MR | Zbl

[2] C. Huber-Carol, F. Vonta, “Frailty models for arbitrarily censored and truncated data”, Lifetime Data Analysis, 10 (2004), 369–388 | DOI | MR | Zbl

[3] C. Huber-Carol, V. Solev, F. Vonta, “Estmation of density for arbitrarily censored and truncated data”, Probability, Statistics, and Modelling in Public Healt, Kluwer Acad. Publ., eds. M. S. Nikulin, D. Commenges, C. Huber-Carol, Springer, New York, 2006, 246–265 | MR

[4] B. W. Turnbull, “The empirical distribution function with arbitrary grouped, censored and truncated data”, J. Royal Statist. Soc., 38 (1976), 290–295 | MR | Zbl