Statistics and Its Interface

Volume 7 (2014)

Number 2

Inference for multivariate mixtures of two unknown symmetric components

Pages: 211 – 217

DOI: http://dx.doi.org/10.4310/SII.2014.v7.n2.a6

Authors

Wenxiu Ge (Department of Statistical Science, Sun Yat-Sen University, Guangzhou, China)

Xiaobo Guo (Department of Statistical Science, Sun Yat-Sen University, Guangzhou, China)

Xueqin Wang (Department of Statistical Science, Sun Yat-Sen University, Guangzhou, China)

Heping Zhang (Department of Statistical Science, Sun Yat-Sen University, Guangzhou, China; Department of Biostatistics, Yale University School of Public Health, New Haven, Connecticut, U.S.A.)

Abstract

Modeling heterogeneity for multivariate data is an important research topic. In this paper, we give a sufficient condition to establish the identifiability for semiparametric multivariate mixture models with unknown location-shifted symmetric components, and propose a novel minimum distance method to estimate the location and proportion parameters. Strong consistency and asymptotic normality of our estimators under some regularity conditions are established. Simulation studies show that the proposed method is robust to misspecified component distributions. The Old Faithful data is also used as a real benchmark to assess the performance of the proposed method.

Keywords

E-distance, identifiability, multivariate symmetry, semiparametric mixtures, V-process

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