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 enjoys a high-efficiency gain compared to classic methods in PLM. Our method is further validated using UK Biobank data by evaluating the risk factors of brain imaging measures.

翻译：完全参数化和线性设定可能不足以捕捉探索复杂特征（如年龄相关脑功能能力变化）的研究中的复杂模式。相比之下，由参数与非参数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，使PLM具备高估计效率。这种整合方案在吸收外部研究中各类简化模型方面具有高度灵活性。理论验证表明所提方法具有理论有效性和计算便捷性，相较于PLM的经典方法实现了显著效率增益。我们进一步利用英国生物银行（UK Biobank）数据，通过评估脑影像测量指标的风险因素验证了该方法。