Nonparametric estimation by convex programming
Juditsky, Anatoli B. ; Nemirovski, Arkadi S.
Ann. Statist., Tome 37 (2009) no. 1, p. 2278-2300 / Harvested from Project Euclid
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The problem we concentrate on is as follows: given (1) a convex compact set X in ℝn, an affine mapping x↦A(x), a parametric family {pμ(⋅)} of probability densities and (2) N i.i.d. observations of the random variable ω, distributed with the density pA(x)(⋅) for some (unknown) x∈X, estimate the value gTx of a given linear form at x. ¶ For several families {pμ(⋅)} with no additional assumptions on X and A, we develop computationally efficient estimation routines which are minimax optimal, within an absolute constant factor. We then apply these routines to recovering x itself in the Euclidean norm.
Publié le : 2009-10-15
Classification:  Estimation of linear functional,  minimax estimation,  oracle inequalities,  convex optimization,  PE tomography,  62G08,  62G15,  62G07 
@article{1247663755,
     author = {Juditsky, Anatoli B. and Nemirovski, Arkadi S.},
     title = {Nonparametric estimation by convex programming},
     journal = {Ann. Statist.},
     volume = {37},
     number = {1},
     year = {2009},
     pages = { 2278-2300},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1247663755}
}

Juditsky, Anatoli B.; Nemirovski, Arkadi S. Nonparametric estimation by convex programming. Ann. Statist., Tome 37 (2009) no. 1, pp.  2278-2300. http://gdmltest.u-ga.fr/item/1247663755/