Asymptotic Normality of Nearest Neighbor Regression Function Estimates
Stute, Winfried
Ann. Statist., Tome 12 (1984) no. 1, p. 917-926 / Harvested from Project Euclid
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Let $(X, Y)$ be a random vector in the plane. We show that a smoothed N.N. estimate of the regression function $m(x) = \mathbb{E}(Y\mid X = x)$ is asymptotically normal under conditions much weaker than needed for the Nadaraya-Watson estimate. It also turns out that N.N. estimates are more efficient than kernel-type estimates if (in the mean) there are few observations in neighborhoods of $x$.
Publié le : 1984-09-14
Classification:  Nearest neighbor estimates,  regression function,  nonparametric estimation,  asymptotic normality,  62J02,  62E20,  62G05 
@article{1176346711,
     author = {Stute, Winfried},
     title = {Asymptotic Normality of Nearest Neighbor Regression Function Estimates},
     journal = {Ann. Statist.},
     volume = {12},
     number = {1},
     year = {1984},
     pages = { 917-926},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176346711}
}

Stute, Winfried. Asymptotic Normality of Nearest Neighbor Regression Function Estimates. Ann. Statist., Tome 12 (1984) no. 1, pp.  917-926. http://gdmltest.u-ga.fr/item/1176346711/