A minimaxity criterion in nonparametric regression based on large-deviations probabilities
Korostelev, Alexander
Ann. Statist., Tome 24 (1996) no. 6, p. 1075-1083 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
A large-deviations criterion is proposed for optimality of nonparametric regression estimators. The criterion is one of minimaxity of the large-deviations probabilities. We study the case where the underlying class of regression functions is either Lipschitz or Hölder, and when the loss function involves estimation at a point or in supremum norm. Exact minimax asymptotics are found in the Gaussian case.
Publié le : 1996-06-14
Classification:  Nonparametric regression,  Gaussian noise,  large-deviations probabilities,  minimax risk,  exact asymptotics,  62G07,  62G20 
@article{1032526957,
     author = {Korostelev, Alexander},
     title = {A minimaxity criterion in nonparametric regression based on large-deviations probabilities},
     journal = {Ann. Statist.},
     volume = {24},
     number = {6},
     year = {1996},
     pages = { 1075-1083},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1032526957}
}

Korostelev, Alexander. A minimaxity criterion in nonparametric regression based on large-deviations probabilities. Ann. Statist., Tome 24 (1996) no. 6, pp.  1075-1083. http://gdmltest.u-ga.fr/item/1032526957/