Density estimation by observations with admixture

O. Sugakova

Department of Theory Probability and Mathematical Statistics, Faculty for Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Academician Glushkov Ave. 2, Build. 7, Kyiv 03127

Abstract: 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.

MSC: Primary 62G07; Secondary 62G20

Language: English

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