Classical latent-score ranking models often fail to distinguish objects' intrinsic scores from contextual effects, which are typically nonlinear and can dominate the observed outcomes. To address this, we introduce a semiparametric ranking framework in which the log-score of each object is modeled as the sum of a utility parameter and a nonparametric covariate effects. Within this framework, we establish model identifiability under mild regularity and connectivity conditions. For estimation, we approximate the covariate effects using a neural network and estimate the parameters via maximum likelihood. Under random design assumptions, we prove that the resulting estimator exists with high probability and derive non-asymptotic error bounds that achieve minimax optimality for both the parametric and nonparametric components. Numerical experiments on both synthetic data and an ATP tennis dataset are conducted to support our findings.

翻译：经典潜在得分排序模型通常难以区分对象的内在得分与环境效应，而环境效应往往是非线性的，甚至可能主导观测结果。为解决此问题，我们提出一种半参数排序框架，其中每个对象的对数得分被建模为一个效用参数与非参数协变量效应的和。在此框架下，我们通过温和的正则性和连通性条件建立了模型的可辨识性。在估计方面，我们利用神经网络近似协变量效应，并通过极大似然法估计参数。在随机设计假设下，我们证明了所得估计量以高概率存在，并推导出参数分量和非参数分量均达到极小极大最优性的非渐近误差界。基于合成数据和ATP网球数据集的数值实验进一步验证了我们的理论结果。