Electronic Journal of Statistics

Flexible estimation of a semiparametric two-component mixture model with one parametric component

Yanyuan Ma and Weixin Yao

Full-text: Open access

Abstract

We study a two-component semiparametric mixture model where one component distribution belongs to a parametric class, while the other is symmetric but otherwise arbitrary. This semiparametric model has wide applications in many areas such as large-scale simultaneous testing/multiple testing, sequential clustering, and robust modeling. We develop a class of estimators that are surprisingly simple and are unique in terms of their construction. A unique feature of these methods is that they do not rely on the estimation of the nonparametric component of the model. Instead, the methods only require a working model of the unspecified distribution, which may or may not reflect the true distribution. In addition, we establish connections between the existing estimator and the new methods and further derive a semiparametric efficient estimator. We compare our estimators with the existing method and investigate the advantages and cost of the relatively simple estimation procedure.

Article information

Source
Electron. J. Statist., Volume 9, Number 1 (2015), 444-474.

Dates
First available in Project Euclid: 24 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1427203125

Digital Object Identifier
doi:10.1214/15-EJS1008

Mathematical Reviews number (MathSciNet)
MR3326131

Zentralblatt MATH identifier
1312.62044

Keywords
Efficiency large-scale simultaneous testing mixture models multiple testing robust statistics semiparametric estimator

Citation

Ma, Yanyuan; Yao, Weixin. Flexible estimation of a semiparametric two-component mixture model with one parametric component. Electron. J. Statist. 9 (2015), no. 1, 444--474. doi:10.1214/15-EJS1008. https://projecteuclid.org/euclid.ejs/1427203125


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