In finite mixture models, we establish the best possible rate of convergence for estimating the mixing distribution. We find that the key for estimating the mixing distribution is the knowledge of the number of components in the mixture. While a $\sqrt n$-consistent rate is achievable when the exact number of components is known, the best possible rate is only $n^{-1/4}$ when it is unknown. Under a strong identifiability condition, it is shown that this rate is reached by some minimum distance estimators. Most commonly used models are found to satisfy the strong identifiability condition.
Publié le : 1995-02-14
Classification:
Local asymptotic normality,
maximum likelihood estimate,
minimum distance,
mixing distribution,
mixture model,
rate of convergence,
strong identifiability,
62G05,
62G20
@article{1176324464,
author = {Chen, Jiahua},
title = {Optimal Rate of Convergence for Finite Mixture Models},
journal = {Ann. Statist.},
volume = {23},
number = {6},
year = {1995},
pages = { 221-233},
language = {en},
url = {http://dml.mathdoc.fr/item/1176324464}
}
Chen, Jiahua. Optimal Rate of Convergence for Finite Mixture Models. Ann. Statist., Tome 23 (1995) no. 6, pp. 221-233. http://gdmltest.u-ga.fr/item/1176324464/