Open Access
May 2020 Robust estimation of mixing measures in finite mixture models
Nhat Ho, XuanLong Nguyen, Ya’acov Ritov
Bernoulli 26(2): 828-857 (May 2020). DOI: 10.3150/18-BEJ1087


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 misspecified kernel settings for any fixed bandwidth. These desirable asymptotic properties are illustrated via careful simulation studies with both synthetic and real data.


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Nhat Ho. XuanLong Nguyen. Ya’acov Ritov. "Robust estimation of mixing measures in finite mixture models." Bernoulli 26 (2) 828 - 857, May 2020.


Received: 1 September 2017; Revised: 1 October 2018; Published: May 2020
First available in Project Euclid: 31 January 2020

zbMATH: 07166549
MathSciNet: MR4058353
Digital Object Identifier: 10.3150/18-BEJ1087

Keywords: Convergence rates , Fisher singularities , minimum distance estimator , Mixture models , model misspecification , Model selection , strong identifiability , superefficiency , Wasserstein distances

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

Vol.26 • No. 2 • May 2020
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