  Gaussian mixture models are widely used to study clustering problems. These
model-based clustering methods require an accurate estimation of the unknown
data density by Gaussian mixtures. In Maugis and Michel (2009), a penalized
maximum likelihood estimator is proposed for automatically selecting the number
of mixture components. In the present paper, a collection of univariate
densities whose logarithm is locally {\beta}-H\"older with moment and tail
conditions are considered. We show that this penalized estimator is minimax
adaptive to the {\beta} regularity of such densities in the Hellinger sense.
