Title: Robust estimation of mixing measures in finite mixture models,
Abstract: In finite mixture models, apart from underlying mixing measure, true kernel
density function of each subpopulation in the data is, in many scenarios,
unknown. Perhaps the most popular approach is to choose some kernel functions
that we empirically believe our data are generated from and use these kernels
to fit our models. Nevertheless, as long as the chosen kernel and the true
kernel are different, statistical inference of mixing measure under this
setting will be highly unstable. To overcome this challenge, we propose
flexible and efficient robust estimators of the mixing measure in these models,
which are inspired by the idea of minimum Hellinger distance estimator, model
selection criteria, and superefficiency phenomenon. We demonstrate that our
estimators consistently recover the true number of components and achieve the
optimal convergence rates of parameter estimation under both the well- and
mis-specified kernel settings for any fixed bandwidth. These desirable
asymptotic properties are illustrated via careful simulation studies with both
synthetic and real data.