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August 1999 Empirical likelihood ratio based confidence intervals for mixture proportions
Jing Qin
Ann. Statist. 27(4): 1368-1384 (August 1999). DOI: 10.1214/aos/1017938930


We consider the problem of estimating a mixture proportion using data from two different distributions as well as from a mixture of them. Under the model assumption that the log-likelihood ratio of the two densities is linear in the observations, we develop an empirical likelihood ratio based statistic for constructing confidence intervals for the mixture proportion. Under some regularity conditions, it is shown that this statistic converges to a chi-squared random variable. Simulation results indicate that the performance of this statistic is satisfactory. As a by-product, we give estimators for the two distribution functions. Connections with case-control studies and discrimination analysis are pointed out.


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Jing Qin. "Empirical likelihood ratio based confidence intervals for mixture proportions." Ann. Statist. 27 (4) 1368 - 1384, August 1999.


Published: August 1999
First available in Project Euclid: 4 April 2002

zbMATH: 0960.62048
MathSciNet: MR1740107
Digital Object Identifier: 10.1214/aos/1017938930

Primary: 62M10
Secondary: 62E20

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.27 • No. 4 • August 1999
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