Semiparametric inference for mixtures of circular data

Autor:	Lacour, Claire, Ngoc, Thanh Mai Pham
Rok vydání:	2021
Předmět:	Mathematics - Statistics Theory
Druh dokumentu:	Working Paper
Popis:	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 $\in$ (0, 1) and f is an unknown density on the circle. In this paper we estimate both the parametric part $\theta$ = (p, R, Q) and the nonparametric part f. The specific problems of identifiability on the circle are studied. A consistent estimator of $\theta$ 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. Comment: Electronic Journal of Statistics , Shaker Heights, OH : Institute of Mathematical Statistics, In press
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2103.07318 Zobrazit plný text záznamu View this record from Arxiv