Bickel and Rosenblatt proposed a procedure for testing the goodness of fit of a specified density to observed data. The test statistic is based on the distance between the kernel density estimate and the hypothesized density, and it depends on a kernel $K$, a bandwidth $b_n$ and an arbitrary weight function $a$. We study the behavior of the asymptotic power of the test and show that a uniform kernel maximizes the power when $a > 0$.
Publié le : 1991-06-14
Classification:
Tests for goodness of fit,
density estimates in tests,
optimal kernel for tests,
smoothed chi-square tests,
asymptotic power,
62G10,
62G20
@article{1176348133,
author = {Ghosh, B. K. and Huang, Wei-Min},
title = {The Power and Optimal Kernel of the Bickel-Rosenblatt Test for Goodness of Fit},
journal = {Ann. Statist.},
volume = {19},
number = {1},
year = {1991},
pages = { 999-1009},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348133}
}
Ghosh, B. K.; Huang, Wei-Min. The Power and Optimal Kernel of the Bickel-Rosenblatt Test for Goodness of Fit. Ann. Statist., Tome 19 (1991) no. 1, pp. 999-1009. http://gdmltest.u-ga.fr/item/1176348133/