A new approach to the stochastic recovery problem
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 1, pp. 36-53
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We consider the problem of minimax estimation of linear functionals on function
classes, also known as the recovery problem. We propose a new
formalization of the original applied problem — in
both deterministic and
stochastic settings. For the latter case we propose
a natural probability measure on the set generated by the
problem's
information operator. We then provides some examples of solving
recovery problems in the new framework and determines the statistical
properties of the stochastic recovery problem's solution. Finally,
we consider an application of the proposed approach to the problem of nonparametric
minimax estimation of the regression function.
Keywords:
recovery problem, a posteriori distribution, nonparametric minimax estimation.
@article{TVP_2004_49_1_a2,
author = {B. S. Darhovsky},
title = {A new approach to the stochastic recovery problem},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {36--53},
publisher = {mathdoc},
volume = {49},
number = {1},
year = {2004},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2004_49_1_a2/}
}
B. S. Darhovsky. A new approach to the stochastic recovery problem. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 1, pp. 36-53. http://geodesic.mathdoc.fr/item/TVP_2004_49_1_a2/