This paper addresses the item ranking problem with associate covariates, focusing on scenarios where the preference scores can not be fully explained by covariates, and the remaining intrinsic scores, are sparse. Specifically, we extend the pioneering Bradley-Terry-Luce (BTL) model by incorporating covariate information and considering sparse individual intrinsic scores. Our work introduces novel model identification conditions and examines the regularized penalized Maximum Likelihood Estimator (MLE) statistical rates. We then construct a debiased estimator for the penalized MLE and analyze its distributional properties. Additionally, we apply our method to the goodness-of-fit test for models with no latent intrinsic scores, namely, the covariates fully explaining the preference scores of individual items. We also offer confidence intervals for ranks. Our numerical studies lend further support to our theoretical findings, demonstrating validation for our proposed method

翻译：本文探讨了带有相关协变量的项目排序问题，重点关注偏好评分无法完全由协变量解释、且剩余内在评分具有稀疏性的场景。具体而言，我们通过引入协变量信息并考虑稀疏的个体内在评分，对开创性的Bradley-Terry-Luce（BTL）模型进行了扩展。本研究提出了新的模型可识别性条件，并考察了正则化惩罚极大似然估计量（MLE）的统计收敛速率。随后，我们构建了惩罚MLE的去偏估计量并分析了其分布特性。此外，我们将所提方法应用于无潜在内在评分模型的拟合优度检验，即协变量完全解释个体项目偏好评分的情形。我们还提供了排序的置信区间。数值研究进一步支持了我们的理论发现，验证了所提出方法的有效性。