Suppose one observes a process V on the unit interval, where $dV = f_o + dW$ with an unknown parameter $f_o \epsilon L_1[0, 1]$ and standard Brownian motion W. We propose a particular test of one-point hypotheses about $f_o$ which is based on suitably standardized increments of V. This test is shown to have desirable consistency properties if, for instance, $f_o$ is restricted to various Hölder classes of functions. The test is mimicked in the context of nonparametric density estimation, nonparametric
regression and interval-censored data. Under shape restrictions on the parameter, such as monotonicity or convexity, we obtain confidence sets for $f_o$ adapting to its unknown smoothness.
Publié le : 1998-02-14
Classification:
Adaptivity,
conditional median,
convexity,
distribution-free,
interval censoring,
modality,
monotonicity,
signs of residuals,
spacings,
62G07,
62G15
@article{1030563987,
author = {D\"umbgen, Lutz},
title = {New goodness-of-fit tests and their application to nonparametric confidence sets},
journal = {Ann. Statist.},
volume = {26},
number = {3},
year = {1998},
pages = { 288-314},
language = {en},
url = {http://dml.mathdoc.fr/item/1030563987}
}
Dümbgen, Lutz. New goodness-of-fit tests and their application to nonparametric confidence sets. Ann. Statist., Tome 26 (1998) no. 3, pp. 288-314. http://gdmltest.u-ga.fr/item/1030563987/