In this paper the asymptotic relative deficiency of the sample $q$-quantile with respect to kernel type estimators of the $q$-quantile is evaluated. The comparison is based on the mean square errors of the estimators. The result suggests a purely analytic measure of performance within the class of kernels. It is notable that a similar situation occurs when kernel estimators of a distribution function are studied.
Publié le : 1984-03-14
Classification:
Sample $q$-quantile,
kernel estimator,
mean square error,
deficiency,
Bahadur approximation,
62G05,
62G20,
62G30
@article{1176346405,
author = {Falk, Michael},
title = {Relative Deficiency of Kernel Type Estimators of Quantiles},
journal = {Ann. Statist.},
volume = {12},
number = {1},
year = {1984},
pages = { 261-268},
language = {en},
url = {http://dml.mathdoc.fr/item/1176346405}
}
Falk, Michael. Relative Deficiency of Kernel Type Estimators of Quantiles. Ann. Statist., Tome 12 (1984) no. 1, pp. 261-268. http://gdmltest.u-ga.fr/item/1176346405/