Semiparametric estimation of a two-component mixture model

• 成果类型: Article
• 署名作者: Bordes, Laurent; Mottelet, Stephane; Vandekerkhove, Pierre
• 署名单位: Universite de Technologie de Compiegne; Universite Gustave-Eiffel
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000353
• 发表日期: 2006
• 页码: 1204-1232
• 关键词: nonparametric-estimation; distributions; likelihood; CONVERGENCE; geometry

摘要

Suppose that univariate data are drawn from a mixture of two distributions that are equal up to a shift parameter. Such a model is known to be nonidentifiable from a nonparametric viewpoint. However, if we assume that the unknown mixed distribution is symmetric, we obtain the identifiability of this model, which is then defined by four unknown parameters: the mixing proportion, two location parameters and the cumulative distribution function of the symmetric mixed distribution. We propose estimators for these four parameters when no training data is available. Our estimators are shown to be strongly consistent under mild regularity assumptions and their convergence rates are studied. Their finite-sample properties are illustrated by a Monte Carlo study and our method is applied to real data.