In this paper, we focus on the partial functional linear model with missing observation, which allows the responses or part of the covariates or responses and part of the covariates simultaneously missing at random, where the regression error is a linear process deduced by not necessarily independent random variables. Under the reproducing kernel Hilbert space setting, we construct the estimators of the slope parameter and coefficient function in the model based on the inverse probability weighting methods, and establish their asymptotic normality and weak convergence with rates, respectively. Meanwhile, the penalized estimator of the parameter is defined by the SCAD penalty and its oracle property is investigated. In addition, we construct a test statistic to check a linear hypothesis of the nonzero parameters and discuss its asymptotic distribution. Simulation study and real data analysis are conducted to investigate the finite sample performance of the proposed methods.

在本文中，我们关注缺失观测的部分函数线性模型，该模型允许响应或部分协变量或响应和部分协变量同时随机缺失，其中回归误差是由不一定独立推导的线性过程随机变量。在再生核Hilbert空间设置下，基于逆概率加权方法构造了模型中斜率参数和系数函数的估计量，并分别建立了它们的渐近正态性和速率的弱收敛性。同时，通过SCAD惩罚定义了参数的惩罚估计量，并研究了其预言性质。此外，我们构造一个检验统计量来检查非零参数的线性假设并讨论其渐近分布。进行仿真研究和实际数据分析来研究所提出方法的有限样本性能。