Random rates in anisotropic regression (with a discussion and a rejoinder by the authors)
Hoffman, M. ; Lepski, O.
Ann. Statist., Tome 30 (2002) no. 1, p. 325-396 / Harvested from Project Euclid
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In the context of minimax theory, we propose a new kind of risk, normalized by a random variable, measurable with respect to the data. We present a notion of optimality and a method to construct optimal procedures accordingly. We apply this general setup to the problem of selecting significant variables in Gaussian white noise. In particular, we show that our method essentially improves the accuracy of estimation, in the sense of giving explicit improved confidence sets in $L_2$-norm. Links to adaptive estimation are discussed.
Publié le : 2002-04-14
Classification:  Nonparametric estimation,  minimax theory,  random normalizing factors,  anisotropic regression,  62G07,  62G10,  62G15 
@article{1021379858,
     author = {Hoffman, M. and Lepski, O.},
     title = {Random rates in anisotropic regression (with a discussion and a
			 rejoinder by the authors)},
     journal = {Ann. Statist.},
     volume = {30},
     number = {1},
     year = {2002},
     pages = { 325-396},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1021379858}
}

Hoffman, M.; Lepski, O. Random rates in anisotropic regression (with a discussion and a
			 rejoinder by the authors). Ann. Statist., Tome 30 (2002) no. 1, pp.  325-396. http://gdmltest.u-ga.fr/item/1021379858/