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Semiparametric inference for mixtures of circular data

Abstract : We consider X 1 ,. .. , X n a sample of data on the circle S 1 , whose distribution is a twocomponent mixture. Denoting R and Q two rotations on S 1 , the density of the X i 's is assumed to be g(x) = pf (R −1 x) + (1 − p)f (Q −1 x), 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.
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https://hal.archives-ouvertes.fr/hal-03149434
Contributor : Claire Lacour Connect in order to contact the contributor
Submitted on : Wednesday, May 25, 2022 - 11:18:41 AM
Last modification on : Saturday, June 25, 2022 - 3:51:33 AM

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  • HAL Id : hal-03149434, version 2
  • ARXIV : 2103.07318

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Claire Lacour, Thanh Mai Pham Ngoc. Semiparametric inference for mixtures of circular data. Electronic Journal of Statistics , Shaker Heights, OH : Institute of Mathematical Statistics, In press. ⟨hal-03149434v2⟩

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