Maiboroda, Rostyslav; Sugakova, Olena Nonparametric density estimation for symmetric distributions by contaminated data. (English) Zbl 1241.62045 Metrika 75, No. 1, 109-126 (2012). Summary: A semiparametric two-component mixture model is considered, in which the distribution of one (primary) component is unknown and assumed to be symmetric. The distribution of the other component (admixture) is known. We consider three estimates for the pdf of the primary component: a naive one, a symmetrized naive estimate and a symmetrized estimate with adaptive weights. Asymptotic behavior and small sample performance of the estimates are investigated. Some rules of thumb for bandwidth selection are discussed. Cited in 5 Documents MSC: 62G07 Density estimation 62G20 Asymptotic properties of nonparametric inference 65C60 Computational problems in statistics (MSC2010) Keywords:asymptotic normality; finite mixture model; symmetric distribution; kernel density estimate; rule of thumb; MISE Software:KernSmooth; mixdist PDFBibTeX XMLCite \textit{R. Maiboroda} and \textit{O. Sugakova}, Metrika 75, No. 1, 109--126 (2012; Zbl 1241.62045) Full Text: DOI References: [1] Bordes L, Delmas C, Vandekerkhove P (2006) Semiparametric estimation of a two-component mixture model where one component is known. Scand J Stat 33: 733–752 · Zbl 1164.62331 · doi:10.1111/j.1467-9469.2006.00515.x [2] Borovkov AA (1998) Mathematical statistics. Gordon and Breach Science Publishers, Amsterdam [3] Bowman AW (1984) An alternative method of cross-validation for the smoothing of density estimates. 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