Efficient estimation using both direct and indirect observations
Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 2, pp. 233-258
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The Ibragimov—Khas'minskii model postulates observing $X_1,\ldots,X_m$ independent, identically distributed according to an unknown distribution $G$ and $Y_1,\ldots,Y_n$ independent and identically distributed according to $\int {k(\,\cdot\,,y)}\,dG(y)$, where $k$ is known, for example, $Y$ is obtained from $X$ by convolution with a Gaussian density. We exhibit sieve type estimates of $G$ which are efficient under minimal conditions which include those of Vardi and Zhang (1992) for the special case, $G$ on $[0,\infty]$, $k(x,y)=y^{-1}1(x\le y)$.
Keywords:
density estimates, parametric estimation, kernel estimates.
@article{TVP_1993_38_2_a2,
author = {P. J. Bickel and Y. Ritov},
title = {Efficient estimation using both direct and indirect observations},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {233--258},
publisher = {mathdoc},
volume = {38},
number = {2},
year = {1993},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1993_38_2_a2/}
}
P. J. Bickel; Y. Ritov. Efficient estimation using both direct and indirect observations. Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 2, pp. 233-258. http://geodesic.mathdoc.fr/item/TVP_1993_38_2_a2/