A full parametric and linear specification may be insufficient to capture complicated patterns in studies exploring complex features, such as those investigating age-related changes in brain functional abilities. Alternatively, a partially linear model (PLM) consisting of both parametric and non-parametric elements may have a better fit. This model has been widely applied in economics, environmental science, and biomedical studies. In this paper, we introduce a novel statistical inference framework that equips PLM with high estimation efficiency by effectively synthesizing summary information from external data into the main analysis. Such an integrative scheme is versatile in assimilating various types of reduced models from the external study. The proposed method is shown to be theoretically valid and numerically convenient, and it ensures a high-efficiency gain compared to classic methods in PLM. Our method is further validated using two data applications by evaluating the risk factors of brain imaging measures and blood pressure.

翻译：完全参数化的线性模型可能难以捕捉复杂特征研究中的复杂模式，例如探究年龄相关脑功能能力变化的研究。而由参数化与非参数化元素构成的部分线性模型（PLM）可能具有更好的拟合效果。该模型已广泛应用于经济学、环境科学和生物医学研究。本文提出了一种新颖的统计推断框架，通过将外部数据的摘要信息有效整合到主分析中，赋予PLM较高的估计效率。这种整合方案能够灵活吸收来自外部研究的各种简化模型。理论证明该方法具有理论有效性和数值便捷性，相较于经典PLM方法可显著提升效率增益。通过在脑影像指标和血压风险因素评估中的两项数据应用，进一步验证了该方法的有效性。