In the mixture of experts model, a common assumption is the linearity between a response variable and covariates. While this assumption has theoretical and computational benefits, it may lead to suboptimal estimates by overlooking potential nonlinear relationships among the variables. To address this limitation, we propose a partially linear structure that incorporates unspecified functions to capture nonlinear relationships. We establish the identifiability of the proposed model under mild conditions and introduce a practical estimation algorithm. We present the performance of our approach through numerical studies, including simulations and real data analysis.

翻译：在混合专家模型中，一个常见假设是响应变量与协变量之间存在线性关系。尽管该假设具有理论和计算上的优势，但忽略变量间潜在的非线性关系可能导致次优估计。为解决这一局限性，我们提出了一种包含未指定函数以捕获非线性关系的部分线性结构。我们在温和条件下建立了所提模型的可识别性，并引入了一种实用的估计算法。通过数值研究（包括模拟实验和实际数据分析），我们展示了该方法的表现。