Risk bounds in isotonic regression
Zhang, Cun-Hui
Ann. Statist., Tome 30 (2002) no. 1, p. 528-555 / Harvested from Project Euclid
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Nonasymptotic risk bounds are provided for maximum likelihood-type isotonic estimators of an unknown nondecreasing regression function, with general average loss at design points. These bounds are optimal up to scale constants, and they imply uniform $n^{-1/3}$-consistency of the $\ell_p$ risk for unknown regression functions of uniformly bounded variation, under mild assumptions on the joint probability distribution of the data, with possibly dependent observations.
Publié le : 2002-04-14
Classification:  Nonparametric regression,  isotonic regression,  risk bounds,  least squares estimator,  maximum likelihood estimator,  62G08,  62G05,  62J02,  62G20 
@article{1021379864,
     author = {Zhang, Cun-Hui},
     title = {Risk bounds in isotonic regression},
     journal = {Ann. Statist.},
     volume = {30},
     number = {1},
     year = {2002},
     pages = { 528-555},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1021379864}
}

Zhang, Cun-Hui. Risk bounds in isotonic regression. Ann. Statist., Tome 30 (2002) no. 1, pp.  528-555. http://gdmltest.u-ga.fr/item/1021379864/