On the Strong Universal Consistency of Nearest Neighbor Regression Function Estimates
Devroye, Luc ; Gyorfi, Laszlo ; Krzyzak, Adam ; Lugosi, Gabor
Ann. Statist., Tome 22 (1994) no. 1, p. 1371-1385 / Harvested from Project Euclid
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Two results are presented concerning the consistency of the $k$-nearest neighbor regression estimate. We show that all modes of convergence in $L_1$ (in probability, almost sure, complete) are equivalent if the regression variable is bounded. Under the additional conditional $k/\log n \rightarrow \infty$ we also obtain the strong universal consistency of the estimate.
Publié le : 1994-09-14
Classification:  Regression function,  nonparametric estimation,  consistency,  strong convergence,  nearest neighbor estimate,  62G05 
@article{1176325633,
     author = {Devroye, Luc and Gyorfi, Laszlo and Krzyzak, Adam and Lugosi, Gabor},
     title = {On the Strong Universal Consistency of Nearest Neighbor Regression Function Estimates},
     journal = {Ann. Statist.},
     volume = {22},
     number = {1},
     year = {1994},
     pages = { 1371-1385},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176325633}
}

Devroye, Luc; Gyorfi, Laszlo; Krzyzak, Adam; Lugosi, Gabor. On the Strong Universal Consistency of Nearest Neighbor Regression Function Estimates. Ann. Statist., Tome 22 (1994) no. 1, pp.  1371-1385. http://gdmltest.u-ga.fr/item/1176325633/