A special semiparametric model for a univariate density is
introduced that allows analyzing a number of problems via appropriate
transformations. Two problems treated in some detail are testing for the
presence of a mixture and detecting a wear-out trend in a failure rate. The
analysis of the semiparametric model leads to an approach that advances the
maximum likelihood theory of the Grenander estimator to a multiscale analysis.
The construction of the corresponding test statistic rests on an extension of a
result on a two-sided Brownian motion with quadratic drift to the simultaneous
control of “excursions under parabolas” at various scales of a
Brownian bridge. The resulting test is shown to be asymptotically optimal in
the minimax sense regarding both rate and constant, and adaptive with respect
to the unknown parameter in the semiparametric model. The performance of the
method is illustrated with a simulation study for the failure rate problem and
with data from a flow cytometry experiment for the mixture analysis.
Publié le : 2001-10-14
Classification:
Multiscale analysis,
Grenander estimator,
minimax,
adaptive,
mixture,
log-concave,
failure rate,
penalized maximum likelihood,
62G10,
60F15
@article{1013203455,
author = {Walther, Guenther},
title = {Multiscale maximum likelihood analysis of a semiparametric
model, with applications},
journal = {Ann. Statist.},
volume = {29},
number = {2},
year = {2001},
pages = { 1297-1319},
language = {en},
url = {http://dml.mathdoc.fr/item/1013203455}
}
Walther, Guenther. Multiscale maximum likelihood analysis of a semiparametric
model, with applications. Ann. Statist., Tome 29 (2001) no. 2, pp. 1297-1319. http://gdmltest.u-ga.fr/item/1013203455/