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The empirical likelihood estimation of the quantile function under the multiplicative intercept risk model

Abstract In the paper, we consider quantile estimation under the multiplicative intercept risk model, which is more general than the case-control two sample density ratio model. Utilizing the auxiliary information in the model, an estimation equation is constructed and a new semi-parametric quantile estimator is proposed by the empirical likelihood method. The consistency and the Bahadur type representation of the quantile estimator are established, where the convergence rate for the residual term in the representation is showed to be .