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June 2000 Quantile estimation under a two-sample semi-parametric model
Biao Zhang
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Bernoulli 6(3): 491-511 (June 2000).


We consider quantile estimation under a two-sample semi-parametric model in which the log ratio of two unknown density functions has a known parametric form. This two-sample semi-parametric model, arising naturally from case-control studies and logistic discriminant analysis, can be regarded as a biased sampling model. A new quantile estimator is constructed on the basis of the maximum semi-parametric likelihood estimator of the underlying distribution function. It is shown that the proposed quantile estimator is asymptotically normally distributed with smaller asymptotic variance than that of the standard quantile estimator. Also presented are some results on simulation and on analysis of a real data set.


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Biao Zhang. "Quantile estimation under a two-sample semi-parametric model." Bernoulli 6 (3) 491 - 511, June 2000.


Published: June 2000
First available in Project Euclid: 10 April 2004

zbMATH: 0957.62027
MathSciNet: MR2001B:62044

Keywords: biased sampling problem , case-control data , Gaussian process , logistic discriminant analysis , logistic regression , relative efficiency , weak convergence

Rights: Copyright © 2000 Bernoulli Society for Mathematical Statistics and Probability


Vol.6 • No. 3 • June 2000
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