Geodesic
Density estimation by observations with admixture
Teoriâ slučajnyh processov, Tome 16 (2010) no. 1, pp. 103-110

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We consider a two-component mixture model, in which the component of interest (the primary component) is assumed to be symmetrically distributed, and the admixture distribution has a known probability density function (pdf). The mixing probability and the mean of the primary component are unknown as well. A kernel estimate for the primary component's pdf is proposed. Under some assumptions, the asymptotic normality of this estimate is demonstrated.
Keywords: Mixture, kernel estimate, Vapnik–Chervonenkis inequality. 
@article{THSP_2010_16_1_a12,
     author = {O. Sugakova},
     title = {Density estimation by observations with admixture},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {103--110},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2010_16_1_a12/}
}
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O. Sugakova. Density estimation by observations with admixture. Teoriâ slučajnyh processov, Tome 16 (2010) no. 1, pp. 103-110. http://geodesic.mathdoc.fr/item/THSP_2010_16_1_a12/