A semiparametric method for estimating densities of normal mean mixtures is presented. This consistent data-driven method of estimation is based on probability spacings. The estimation technique involves iteratively fixing the standard deviation of the normal kernel that serves as a smoothing parameter, and then maximizing a function of the probability spacings over all mixing distributions. Based on the distribution of uniform spacings, a distribution free goodness-of-fit criterion is developed to guide the selection of the smoothing parameter. The result is a set of consistent estimators indexed by a range of smoothing parameters. Empirical process results are used to prove consistency.
Publié le : 1992-06-14
Classification:
Confidence set of densities,
normal mixtures,
semiparametric density estimation,
spacings,
62G05,
62G30,
62E20
@article{1176348664,
author = {Roeder, Kathryn},
title = {Semiparametric Estimation of Normal Mixture Densities},
journal = {Ann. Statist.},
volume = {20},
number = {1},
year = {1992},
pages = { 929-943},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348664}
}
Roeder, Kathryn. Semiparametric Estimation of Normal Mixture Densities. Ann. Statist., Tome 20 (1992) no. 1, pp. 929-943. http://gdmltest.u-ga.fr/item/1176348664/