We establish the validity of bootstrap methods for empirical likelihood (EL) inference under the density ratio model (DRM). In particular, we prove that the bootstrap maximum EL estimators share the same limiting distribution as their population counterparts, both at the parameter level and for distribution functionals. Our results extend existing pointwise convergence theory to weak convergence of processes, which in turn justifies bootstrap inference for quantiles and dominance indices within the DRM framework. These theoretical guarantees close an important gap in the literature, providing rigorous foundations for resampling-based confidence intervals and hypothesis tests. Simulation studies further demonstrate the accuracy and practical value of the proposed approach.

翻译：本文确立了密度比模型下经验似然推断中自举方法的有效性。具体而言，我们证明了自举最大经验似然估计量在参数层面及分布泛函上均与其总体对应量具有相同的极限分布。我们的结果将现有的逐点收敛理论推广至过程的弱收敛，从而为密度比模型框架下的分位数与优势指数推断提供了自举方法的理论依据。这些理论保证填补了文献中的一个重要空白，为基于重采样的置信区间与假设检验提供了严格的理论基础。模拟研究进一步验证了所提方法的准确性与实用价值。