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2013 Two-component mixtures with independent coordinates as conditional mixtures: Nonparametric identification and estimation
Daniel Hohmann, Hajo Holzmann
Electron. J. Statist. 7: 859-880 (2013). DOI: 10.1214/13-EJS792

Abstract

We show how the multivariate two-component mixtures with independent coordinates in each component by Hall and Zhou (2003) can be studied within the framework of conditional mixtures as recently introduced by Henry, Kitamura and Salanié (2010). Here, the conditional distribution of the random variable $Y$ given the vector of regressors $Z$ can be expressed as a two-component mixture, where only the mixture weights depend on the covariates. Under appropriate tail conditions on the characteristic functions and the distribution functions of the mixture components, which allow for flexible location-scale type mixtures, we show identification and provide asymptotically normal estimators. The main application for our results are bivariate two-component mixtures with independent coordinates, the case not previously covered by Hall and Zhou (2003). In a simulation study we investigate the finite-sample performance of the proposed methods. The main new technical ingredient is the estimation of limits of quotients of two characteristic functions in the tails from independent samples, which might be of some independent interest.

Citation

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Daniel Hohmann. Hajo Holzmann. "Two-component mixtures with independent coordinates as conditional mixtures: Nonparametric identification and estimation." Electron. J. Statist. 7 859 - 880, 2013. https://doi.org/10.1214/13-EJS792

Information

Published: 2013
First available in Project Euclid: 3 April 2013

zbMATH: 1337.62056
MathSciNet: MR3044502
Digital Object Identifier: 10.1214/13-EJS792

Subjects:
Primary: 62G05, 62G20

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society

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