Open Access
2022 Semiparametric inference for mixtures of circular data
Claire Lacour, Thanh Mai Pham Ngoc
Author Affiliations +
Electron. J. Statist. 16(1): 3482-3522 (2022). DOI: 10.1214/22-EJS2024


We consider X1,,Xn a sample of data on the circle S1, whose distribution is a two-component mixture. Denoting R and Q two rotations on S1, the density of the Xi’s is assumed to be g(x)=pf(R1x)+(1p)f(Q1x), where p(0,1) and f is an unknown density on the circle. In this paper we estimate both the parametric part θ=(p,R,Q) and the nonparametric part f. The specific problems of identifiability on the circle are studied. A consistent estimator of θ is introduced and its asymptotic normality is proved. We propose a Fourier-based estimator of f with a penalized criterion to choose the resolution level. We show that our adaptive estimator is optimal from the oracle and minimax points of view when the density belongs to a Sobolev ball. Our method is illustrated by numerical simulations.


The authors would like to thank the Editors and one anonymous referee for valuable comments and suggestions leading to corrections and improvements of the article.


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Claire Lacour. Thanh Mai Pham Ngoc. "Semiparametric inference for mixtures of circular data." Electron. J. Statist. 16 (1) 3482 - 3522, 2022.


Received: 1 February 2021; Published: 2022
First available in Project Euclid: 25 May 2022

MathSciNet: MR4429527
zbMATH: 1493.62289
Digital Object Identifier: 10.1214/22-EJS2024

Primary: 62G05 , 62H11 , 62H30

Keywords: Circular data , mixture model , Semiparametric estimation

Vol.16 • No. 1 • 2022
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