In this paper, we are concerned with nonlinear interaction detection based on partial dimension reduction with missing response data. The covariates are grouped through linear combinations in a general class of semi-parametric models to detect their joint interaction effects. The joint interaction effects are estimated by a profile least squares approach with the help of the inverse probability weighted technique. The asymptotic properties of the resulting estimate for the central partial mean subspace are established. In addition, a Wald type test is proposed to detect the interactions between the covariates. A BIC-type criterion is applied to determine the structural dimension of the central partial mean subspace and its consistency is also obtained. Simulations are conducted to examine the finite sample performances of our proposed method and a real data set is analyzed for illustration.

在本文中，我们关注基于部分降维和缺失响应数据的非线性交互检测。协变量通过一般类半参数模型中的线性组合进行分组，以检测它们的联合交互作用。在逆概率加权技术的帮助下，通过剖面最小二乘法估计联合交互作用。建立了中心部分均值子空间的结果估计的渐近特性。此外，还提出了 Wald 型检验来检测协变量之间的相互作用。应用 BIC 型准则来确定中心部分均值子空间的结构维数，并获得其一致性。