In both density and regression estimation problems, the $k$-nearest neighbor estimators with $k$ varying in an appropriate range, when transformed to continuous time stochastic processes, are shown to have a common limiting structure under the usual second-order smoothness conditions as the sample size tends to $\infty$. These results lead to asymptotic linear models in which BLUE's and suitably biased linear combinations are considered.
Publié le : 1987-09-14
Classification:
Density estimation,
regression estimation,
nearest neighbor,
asymptotic linear model,
order statistics,
induced order statistics,
weak convergence,
62G05,
62J02,
62G20,
62G30,
60F17
@article{1176350487,
author = {Bhattacharya, P. K. and Mack, Y. P.},
title = {Weak Convergence of $k$-NN Density and Regression Estimators with Varying $k$ and Applications},
journal = {Ann. Statist.},
volume = {15},
number = {1},
year = {1987},
pages = { 976-994},
language = {en},
url = {http://dml.mathdoc.fr/item/1176350487}
}
Bhattacharya, P. K.; Mack, Y. P. Weak Convergence of $k$-NN Density and Regression Estimators with Varying $k$ and Applications. Ann. Statist., Tome 15 (1987) no. 1, pp. 976-994. http://gdmltest.u-ga.fr/item/1176350487/