Quantile estimation under a two-sample semi-parametric model

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 from the analysis of a real data set.