A semiparametric density estimation is proposed under a two-sample density ratio model. This model, arising naturally from case-control studies and logistic discriminant analyses, can also be regarded as a biased sampling model. Our proposed density estimate is therefore an extension of the kernel density estimate suggested by Jones for length-biased data. We show that under the model considered the new density estimator not only is consistent but also has the `smallest' asymptotic variance among general nonparametric density estimators. We also show how to use the new estimate to define a procedure for testing the goodness of fit of the density ratio model. Such a test is consistent under very general alternatives. Finally, we present some results from simulations and from the analysis of two real data sets.
Publié le : 2004-08-14
Classification:
asymptotic relative efficiency,
biased sampling problem,
case-control data,
density estimation,
goodness-of-fit test,
logistic regression,
semiparametric maximum likelihood estimation
@article{1093265631,
author = {Cheng, K.F. and Chu, C.K.},
title = {Semiparametric density estimation under a two-sample density ratio model},
journal = {Bernoulli},
volume = {10},
number = {2},
year = {2004},
pages = { 583-604},
language = {en},
url = {http://dml.mathdoc.fr/item/1093265631}
}
Cheng, K.F.; Chu, C.K. Semiparametric density estimation under a two-sample density ratio model. Bernoulli, Tome 10 (2004) no. 2, pp. 583-604. http://gdmltest.u-ga.fr/item/1093265631/